computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
software
Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work.
At the lowest programming level, executable code consists ...
and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design.
Formal methods employ a variety of
theoretical computer science
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory.
It is difficult to circumsc ...
fundamentals, including
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
calculi,
formal language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.
The alphabet of a formal language consists of symb ...
control theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
type systems
In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type (computer science), type to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constru ...
, and
type theory
In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundat ...
.
Background
Semi-Formal Methods are formalisms and languages that are not considered fully “formal”. It defers the task of completing the semantics to a later stage, which is then done either by human interpretation or by interpretation through software like code or test case generators.
Taxonomy
Formal methods can be used at a number of levels:
Level 0: Formal specification may be undertaken and then a program developed from this informally. This has been dubbed ''formal methods lite''. This may be the most cost-effective option in many cases.
Level 1: Formal development and
formal verification
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal metho ...
may be used to produce a program in a more formal manner. For example, proofs of properties or
refinement
Refinement may refer to: Mathematics
* Equilibrium refinement, the identification of actualized equilibria in game theory
* Refinement of an equivalence relation, in mathematics
** Refinement (topology), the refinement of an open cover in mathem ...
from the specification to a program may be undertaken. This may be most appropriate in high-integrity systems involving
safety
Safety is the state of being "safe", the condition of being protected from harm or other danger. Safety can also refer to risk management, the control of recognized hazards in order to achieve an acceptable level of risk.
Meanings
There are ...
or
security
Security is protection from, or resilience against, potential harm (or other unwanted coercive change) caused by others, by restraining the freedom of others to act. Beneficiaries (technically referents) of security may be of persons and social ...
.
Level 2: Theorem provers may be used to undertake fully formal machine-checked proofs. Despite improving tools and declining costs, this can be very expensive and is only practically worthwhile if the cost of mistakes is very high (e.g., in critical parts of operating system or microprocessor design).
Further information on this is expanded
below
Below may refer to:
*Earth
*Ground (disambiguation)
*Soil
*Floor
*Bottom (disambiguation)
Bottom may refer to:
Anatomy and sex
* Bottom (BDSM), the partner in a BDSM who takes the passive, receiving, or obedient role, to that of the top or ...
.
As with
programming language semantics
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax.
Semantics describes the processe ...
, styles of formal methods may be roughly classified as follows:
*
Denotational semantics
In computer science, denotational semantics (initially known as mathematical semantics or Scott–Strachey semantics) is an approach of formalizing the meanings of programming languages by constructing mathematical objects (called ''denotations'' ...
, in which the meaning of a system is expressed in the mathematical theory of domains. Proponents of such methods rely on the well-understood nature of domains to give meaning to the system; critics point out that not every system may be intuitively or naturally viewed as a function.
* Operational semantics, in which the meaning of a system is expressed as a sequence of actions of a (presumably) simpler computational model. Proponents of such methods point to the simplicity of their models as a means to expressive clarity; critics counter that the problem of semantics has just been delayed (who defines the semantics of the simpler model?).
*
Axiomatic semantics
Axiomatic semantics is an approach based on mathematical logic for proving the correctness of computer programs. It is closely related to Hoare logic.
Axiomatic semantics define the meaning of a command in a program by describing its effect on ass ...
, in which the meaning of the system is expressed in terms of preconditions and postconditions which are true before and after the system performs a task, respectively. Proponents note the connection to classical
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
; critics note that such semantics never really describe what a system ''does'' (merely what is true before and afterwards).
Lightweight formal methods
Some practitioners believe that the formal methods community has overemphasized full formalization of a specification or design. They contend that the expressiveness of the languages involved, as well as the complexity of the systems being modelled, make full formalization a difficult and expensive task. As an alternative, various ''lightweight'' formal methods, which emphasize partial specification and focused application, have been proposed. Examples of this lightweight approach to formal methods include the
Alloy
An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductility, ...
object modelling notation, Denney's synthesis of some aspects of the
Z notation
The Z notation is a formal specification language used for describing and modelling computing systems. It is targeted at the clear specification of computer programs and computer-based systems in general.
History
In 1974, Jean-Raymond Abrial ...
with
use case
In software and systems engineering, the phrase use case is a polyseme with two senses:
# A usage scenario for a piece of software; often used in the plural to suggest situations where a piece of software may be useful.
# A potential scenario ...
Formal methods can be applied at various points through the development process.
Specification
Formal methods may be used to give a description of the system to be developed, at whatever level(s) of detail desired. This formal description can be used to guide further development activities (see following sections); additionally, it can be used to verify that the requirements for the system being developed have been completely and accurately specified, or formalising system requirements by expressing them in a formal language with a precise and unambiguously defined syntax and semantics.
The need for formal specification systems has been noted for years. In the ALGOL 58 report, John Backus presented a formal notation for describing programming language syntax, later named
Backus normal form
Backus is a middle English surname deriving from the Old English bacan "to bake" and hus "house." It is believed to have originated in the north English historic counties of Cumberland and Durham.
People
Notable people with the surname include:
...
then renamed
Backus–Naur form
In computer science, Backus–Naur form () or Backus normal form (BNF) is a metasyntax notation for context-free grammars, often used to describe the syntax of languages used in computing, such as computer programming languages, document formats ...
(BNF). Backus also wrote that a formal description of the meaning of syntactically valid ALGOL programs wasn't completed in time for inclusion in the report. "Therefore the formal treatment of the semantics of legal programs will be included in a subsequent paper." It never appeared.
Development
Formal development is the use of formal methods as an integrated part of a tool-supported system development process.
Once a formal specification has been produced, the specification may be used as a guide while the concrete system is developed during the
design
A design is a plan or specification for the construction of an object or system or for the implementation of an activity or process or the result of that plan or specification in the form of a prototype, product, or process. The verb ''to design'' ...
process (i.e., realized typically in software, but also potentially in hardware). For example:
* If the formal specification is in operational semantics, the observed behavior of the concrete system can be compared with the behavior of the specification (which itself should be executable or simulatable). Additionally, the operational commands of the specification may be amenable to direct translation into executable code.
* If the formal specification is in axiomatic semantics, the preconditions and postconditions of the specification may become assertions in the executable code.
Verification
Formal verification is the use of software tools to prove properties of a formal specification, or to prove that a formal model of a system implementation satisfies its specification.
Once a formal specification has been developed, the specification may be used as the basis for proving properties of the specification, and by inference, properties of the system implementation.
Sign-off verification
Sign-off verification is the use of a formal verification tool that is highly trusted. Such a tool can replace traditional verification methods (the tool may even be certified).
Human-directed proof
Sometimes, the motivation for proving the correctness of a system is not the obvious need for reassurance of the correctness of the system, but a desire to understand the system better. Consequently, some proofs of correctness are produced in the style of
mathematical proof
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proo ...
: handwritten (or typeset) using
natural language
In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages ...
, using a level of informality common to such proofs. A "good" proof is one that is readable and understandable by other human readers.
Critics of such approaches point out that the
ambiguity
Ambiguity is the type of meaning in which a phrase, statement or resolution is not explicitly defined, making several interpretations plausible. A common aspect of ambiguity is uncertainty. It is thus an attribute of any idea or statement ...
inherent in natural language allows errors to be undetected in such proofs; often, subtle errors can be present in the low-level details typically overlooked by such proofs. Additionally, the work involved in producing such a good proof requires a high level of mathematical sophistication and expertise.
Automated proof
In contrast, there is increasing interest in producing proofs of correctness of such systems by automated means. Automated techniques fall into three general categories:
*
Automated theorem proving
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a maj ...
, in which a system attempts to produce a formal proof from scratch, given a description of the system, a set of logical axioms, and a set of inference rules.
*
Model checking
In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically associated with hardware or software systems ...
, in which a system verifies certain properties by means of an exhaustive search of all possible states that a system could enter during its execution.
*
Abstract interpretation
In computer science, abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial execution of a computer prog ...
, in which a system verifies an over-approximation of a behavioural property of the program, using a fixpoint computation over a (possibly complete) lattice representing it.
Some automated theorem provers require guidance as to which properties are "interesting" enough to pursue, while others work without human intervention. Model checkers can quickly get bogged down in checking millions of uninteresting states if not given a sufficiently abstract model.
Proponents of such systems argue that the results have greater mathematical certainty than human-produced proofs, since all the tedious details have been algorithmically verified. The training required to use such systems is also less than that required to produce good mathematical proofs by hand, making the techniques accessible to a wider variety of practitioners.
Critics note that some of those systems are like
oracle
An oracle is a person or agency considered to provide wise and insightful counsel or prophetic predictions, most notably including precognition of the future, inspired by deities. As such, it is a form of divination.
Description
The word '' ...
s: they make a pronouncement of truth, yet give no explanation of that truth. There is also the problem of " verifying the verifier"; if the program which aids in the verification is itself unproven, there may be reason to doubt the soundness of the produced results. Some modern model checking tools produce a "proof log" detailing each step in their proof, making it possible to perform, given suitable tools, independent verification.
The main feature of the abstract interpretation approach is that it provides a sound analysis, i.e. no false negatives are returned. Moreover, it is efficiently scalable, by tuning the abstract domain representing the property to be analyzed, and by applying widening operators to get fast convergence.
Applications
Formal methods are applied in different areas of hardware and software, including routers, Ethernet switches, routing protocols, security applications, and operating system microkernels such as
seL4
L4 is a family of second-generation microkernels, used to implement a variety of types of operating systems (OS), though mostly for Unix-like, ''Portable Operating System Interface'' (POSIX) compliant types.
L4, like its predecessor microkernel ...
. There are several examples in which they have been used to verify the functionality of the hardware and software used in DCs. IBM used
ACL2
ACL2 ("A Computational Logic for Applicative Common Lisp") is a software system consisting of a programming language, created by Timothy Still it was an extensible theory in a first-order logic, and an automated theorem prover. ACL2 is designed to ...
, a theorem prover, in the
AMD
Advanced Micro Devices, Inc. (AMD) is an American multinational semiconductor company based in Santa Clara, California, that develops computer processors and related technologies for business and consumer markets. While it initially manufactur ...
x86 processor development process. Intel uses such methods to verify its hardware and firmware (permanent software programmed into a read-only memory).
Dansk Datamatik Center
Dansk Datamatik Center (DDC) was a Danish software research and development centre that existed from 1979 to 1989. Its main purpose was to demonstrate the value of using modern techniques, especially those involving formal methods, in software ...
used formal methods in the 1980s to develop a compiler system for the Ada programming language that went on to become a long-lived commercial product.
There are several other projects of
NASA
The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research.
NASA was established in 1958, succeeding t ...
in which formal methods are applied, such as
Next Generation Air Transportation System
The Next Generation Air Transportation System (NextGen) is an ongoing United States Federal Aviation Administration (FAA) project to modernize the National Airspace System (NAS). The FAA began work on NextGen improvements in 2007 and plans to finis ...
, Unmanned Aircraft System integration in National Airspace System, and Airborne Coordinated Conflict Resolution and Detection (ACCoRD).
B-Method with Atelier B, is used to develop safety automatisms for the various subways installed throughout the world by
Alstom
Alstom SA is a French multinational rolling stock manufacturer operating worldwide in rail transport markets, active in the fields of passenger transportation, signalling, and locomotives, with products including the AGV, TGV, Eurostar, Avelia ...
and
Siemens
Siemens AG ( ) is a German multinational conglomerate corporation and the largest industrial manufacturing company in Europe headquartered in Munich with branch offices abroad.
The principal divisions of the corporation are ''Industry'', '' ...
, and also for
Common Criteria
The Common Criteria for Information Technology Security Evaluation (referred to as Common Criteria or CC) is an international standard (ISO/IEC 15408) for computer security certification. It is currently in version 3.1 revision 5.
Common Criteria ...
certification and the development of system models by
ATMEL
Atmel Corporation was a creator and manufacturer of semiconductors before being subsumed by Microchip Technology in 2016. Atmel was founded in 1984. The company focused on embedded systems built around microcontrollers. Its products included micr ...
and
STMicroelectronics
STMicroelectronics N.V. commonly referred as ST or STMicro is a Dutch multinational corporation and technology company of French-Italian origin headquartered in Plan-les-Ouates near Geneva, Switzerland and listed on the French stock market. ST ...
.
Formal verification has been frequently used in hardware by most of the well-known hardware vendors, such as IBM,
Intel
Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California. It is the world's largest semiconductor chip manufacturer by revenue, and is one of the developers of the x86 seri ...
, and AMD. There are many areas of hardware, where Intel have used FMs to verify the working of the products, such as parameterized verification of cache-coherent protocol, Intel Core i7 processor execution engine validation (using theorem proving, BDDs, and symbolic evaluation), optimization for Intel IA-64 architecture using HOL light theorem prover, and verification of high-performance dual-port gigabit Ethernet controller with support for PCI express protocol and Intel advance management technology using Cadence. Similarly, IBM has used formal methods in the verification of power gates, registers, and functional verification of the IBM Power7 microprocessor.
In software development
In
software development
Software development is the process of conceiving, specifying, designing, programming, documenting, testing, and bug fixing involved in creating and maintaining applications, frameworks, or other software components. Software development invol ...
, formal methods are mathematical approaches to solving software (and hardware) problems at the requirements, specification, and design levels. Formal methods are most likely to be applied to safety-critical or security-critical software and systems, such as
avionics software
Avionics software is embedded software with legally mandated safety and reliability concerns used in avionics. The main difference between avionic software and conventional embedded software is that the development process is ''required by law' ...
. Software safety assurance standards, such as DO-178C allows the usage of formal methods through supplementation, and
Common Criteria
The Common Criteria for Information Technology Security Evaluation (referred to as Common Criteria or CC) is an international standard (ISO/IEC 15408) for computer security certification. It is currently in version 3.1 revision 5.
Common Criteria ...
mandates formal methods at the highest levels of categorization.
For sequential software, examples of formal methods include the B-Method, the specification languages used in
automated theorem proving
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a maj ...
,
RAISE
Raise may refer to:
Music
*''Raise!'', the name of a 1981 album by Earth, Wind, and Fire
* '' Raise'' (album), the name of a 1991 album by Swervedriver
Place names
* Raise, Cumbria, England
* Raise (Lake District), the name of the 12th highe ...
, and the
Z notation
The Z notation is a formal specification language used for describing and modelling computing systems. It is targeted at the clear specification of computer programs and computer-based systems in general.
History
In 1974, Jean-Raymond Abrial ...
.
In
functional programming
In computer science, functional programming is a programming paradigm where programs are constructed by Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declar ...
, property-based testing has allowed the mathematical specification and testing (if not exhaustive testing) of the expected behaviour of individual functions.
The Object Constraint Language (and specializations such as
Java Modeling Language The Java Modeling Language (JML) is a specification language for Java programs, using Hoare style pre- and postconditions and invariants, that follows the design by contract paradigm. Specifications are written as Java annotation comments to th ...
) has allowed object-oriented systems to be formally specified, if not necessarily formally verified.
For concurrent software and systems, Petri nets,
process algebra
In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems. Process calculi provide a tool for the high-level description of interactions, communications, and ...
event driven finite state machine
In computation, a finite-state machine (FSM) is event driven if the transition from one state to another is triggered by an event or a message. This is in contrast to the parsing-theory origins of the term finite-state machine where the machine ...
) allow executable software specification and can be used to build up and validate application behaviour.
Another approach to formal methods in software development is to write a specification in some form of logic—usually a variation of first-order logic (FOL)—and then to directly execute the logic as though it were a program. The OWL language, based on Description Logic (DL), is an example. There is also work on mapping some version of English (or another natural language) automatically to and from logic, as well as executing the logic directly. Examples are Attempto Controlled English, and Internet Business Logic, which do not seek to control the vocabulary or syntax. A feature of systems that support bidirectional English-logic mapping and direct execution of the logic is that they can be made to explain their results, in English, at the business or scientific level.
Formal methods and notations
There are a variety of formal methods and notations available.
Specification languages
*
Abstract State Machines
In computer science, an abstract state machine (ASM) is a state machine operating on states that are arbitrary data structures (structure in the sense of mathematical logic, that is a nonempty set together with a number of functions ( operations ...
Actor model
The actor model in computer science is a mathematical model of concurrent computation that treats ''actor'' as the universal primitive of concurrent computation. In response to a message it receives, an actor can: make local decisions, create more ...
*
Alloy
An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductility, ...
Java Modeling Language The Java Modeling Language (JML) is a specification language for Java programs, using Hoare style pre- and postconditions and invariants, that follows the design by contract paradigm. Specifications are written as Java annotation comments to th ...
Lustre
Lustre or Luster may refer to:
Places
* Luster, Norway, a municipality in Vestlandet, Norway
** Luster (village), a village in the municipality of Luster
* Lustre, Montana, an unincorporated community in the United States
Entertainment
* '' ...
Predicative programming Predicative programming is the original name of a formal method for program specification language, specification and program refinement, refinement, more recently called a Practical Theory of Programming, invented by Eric Hehner. The central idea i ...
π-calculus
In theoretical computer science, the -calculus (or pi-calculus) is a process calculus. The -calculus allows channel names to be communicated along the channels themselves, and in this way it is able to describe concurrent computations whose networ ...
*
RAISE
Raise may refer to:
Music
*''Raise!'', the name of a 1981 album by Earth, Wind, and Fire
* '' Raise'' (album), the name of a 1991 album by Swervedriver
Place names
* Raise, Cumbria, England
* Raise (Lake District), the name of the 12th highe ...
*
Rebeca Modeling Language
Rebeca (acronym for Reactive Objects Language) is an actor-based modeling language with a formal foundation, designed in an effort to bridge the gap between formal verification approaches and real applications. It can be considered as a reference ...
USL
The USL Championship (USLC) is a professional men's soccer league in the United States that began its inaugural season in 2011. The USL is sanctioned by the United States Soccer Federation (U.S. Soccer) as a Division II league since 2017, p ...
Z notation
The Z notation is a formal specification language used for describing and modelling computing systems. It is targeted at the clear specification of computer programs and computer-based systems in general.
History
In 1974, Jean-Raymond Abrial ...
Model checkers
* ESBMC
*
MALPAS Software Static Analysis Toolset
MALPAS is a software toolset that provides a means of investigating and proving the correctness of software by applying a rigorous form of static program analysis. The tool uses directed graphs and regular algebra to represent the program under ...
– an industrial-strength model checker used for formal proof of safety-critical systems
* PAT – a free model checker, simulator and refinement checker for concurrent systems and CSP extensions (e.g., shared variables, arrays, fairness)
*
SPIN
Spin or spinning most often refers to:
* Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning
* Spin, the rotation of an object around a central axis
* Spin (propaganda), an intentionally b ...
BCS-FACS
BCS-FACS is the BCS ''Formal Aspects of Computing Science'' Specialist Group.
Overview
The FACS group, inaugurated on 16 March 1978, organizes meetings for its members and others on formal methods and related computer science topics. There is a ...
*
Formal Methods Europe Formal Methods Europe (FME) is an organization whose aim is to encourage the research and application of formal methods for the improvement of software and hardware in computer-based systems. The association's members are drawn from academia and in ...
Abstract interpretation
In computer science, abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial execution of a computer prog ...
*
Automated theorem proving
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a maj ...
Formal methods people
Formal, formality, informal or informality imply the complying with, or not complying with, some set of requirements (forms, in Ancient Greek). They may refer to:
Dress code and events
* Formal wear, attire for formal events
* Semi-formal attire ...
Formal verification
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal metho ...
*
Formal system
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system.
A form ...
*
Model checking
In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically associated with hardware or software systems ...
*
Software engineering
Software engineering is a systematic engineering approach to software development.
A software engineer is a person who applies the principles of software engineering to design, develop, maintain, test, and evaluate computer software. The term '' ...
* Jonathan P. Bowen and Michael G. Hinchey, ''Formal Methods''. In Allen B. Tucker, Jr. (ed.), ''Computer Science Handbook'', 2nd edition, Section XI, ''Software Engineering'', Chapter 106, pages 106-1 – 106-25, Chapman & Hall /
CRC Press
The CRC Press, LLC is an American publishing group that specializes in producing technical books. Many of their books relate to engineering, science and mathematics. Their scope also includes books on business, forensics and information tec ...
,
Association for Computing Machinery
The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional member ...
Bundesamt für Sicherheit in der Informationstechnik
The Federal Office for Information Security (german: Bundesamt für Sicherheit in der Informationstechnik, abbreviated as BSI) is the German upper-level federal agency in charge of managing computer and communication security for the German go ...
, BSI study 875, Bonn, Germany, December 2013.
* * Michael G. Hinchey, Jonathan P. Bowen, and Emil Vassev, ''Formal Methods''. In Philip A. Laplante (ed.), ''Encyclopedia of Software Engineering'',
Taylor & Francis
Taylor & Francis Group is an international company originating in England that publishes books and academic journals. Its parts include Taylor & Francis, Routledge, F1000 (publisher), F1000 Research or Dovepress. It is a division of Informa ...
, 2010, pages 308–320.
*
Marieke Huisman
Marieke Huisman (born 3 May 1973, Utrecht, Netherlands) is a Dutch Computer Scientist and a professor of ''Software Reliability'' at the University of Twente, where she leads the ''Formal Methods and Tools'' Group.
Career
Huisman graduated ...
Michael G. Hinchey
Michael Gerard Hinchey (born 1969) is an Irish computer scientist and former Director of the Irish Software Engineering Research Centre (Lero), a multi-university research centre headquartered at the University of Limerick, Ireland.Springer, 2003, .
Archive.org
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
Archive.org
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...