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Program Correctness
In theoretical computer science, an algorithm is correct with respect to a specification if it behaves as specified. Best explored is ''functional'' correctness, which refers to the input-output behavior of the algorithm (i.e., for each input it produces an output satisfying the specification). Within the latter notion, ''partial correctness'', requiring that ''if'' an answer is returned it will be correct, is distinguished from ''total correctness'', which additionally requires that an answer ''is'' eventually returned, i.e. the algorithm terminates. Correspondingly, to prove a program's total correctness, it is sufficient to prove its partial correctness, and its termination. The latter kind of proof (termination proof) can never be fully automated, since the halting problem is undecidable. For example, successively searching through integers 1, 2, 3, … to see if we can find an example of some phenomenon—say an odd perfect number—it is quite easy to write a par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 circumscribe the theoretical areas precisely. The Association for Computing Machinery, ACM's ACM SIGACT, Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved. Information theory was added to the field with a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of Hebbian learning, learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Theory
Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Jon Barwise, Barwise (1978) consists of four corresponding parts, with part D being about "Proof Theory and Constructive Mathematics". of mathematical logic that represents Mathematical proof, proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as Recursive data type, inductively-defined data structures such as list (computer science), lists, boxed lists, or Tree (data structure), trees, which are constructed according to the axioms and rule of inference, rules of inference of the logical system. Consequently, proof theory is syntax (logic), syntactic in nature, in contrast to model theory, which is Formal semantics (logic), semantic in nature. Some of the major areas of proof theory include structural proof theory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Methods Terminology
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, attire for semi-formal events * Informal attire, more controlled attire than casual but less than formal * Formal (university), official university dinner, ball or other event * School formal, official school dinner, ball or other event Logic and mathematics *Formal logic, or mathematical logic ** Informal logic, the complement, whose definition and scope is contentious *Formal fallacy, reasoning of invalid structure ** Informal fallacy, the complement *Informal mathematics, also called naïve mathematics *Formal cause, Aristotle's intrinsic, determining cause *Formal power series, a generalization of power series without requiring convergence, used in combinatorics *Formal calculation, a calculation which is systematic, but without a r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Program Derivation
In computer science, program derivation is the derivation of a program from its specification, by mathematical means. To ''derive'' a program means to write a formal specification, which is usually non-executable, and then apply mathematically correct rules in order to obtain an executable program satisfying that specification. The program thus obtained is then correct by construction. Program and correctness proof are constructed together. The approach usually taken in formal verification is to first write a program, and then provide a proof that it conforms to a given specification. The main problems with this are that * the resulting proof is often long and cumbersome; * no insight is given as to how the program was developed; it appears "like a rabbit out of a hat"; * should the program happen to be incorrect in some subtle way, the attempt to verify it is likely to be long and certain to be fruitless. Program derivation tries to remedy these shortcomings by * keeping proo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compiler Correctness
In computing, compiler correctness is the branch of computer science that deals with trying to show that a compiler behaves according to its language specification. Techniques include developing the compiler using formal methods and using rigorous testing (often called compiler validation) on an existing compiler. Formal verification Two main formal verification approaches for establishing correctness of compilation are proving correctness of the compiler for all inputs and proving correctness of a compilation of a particular program (translation validation). Compiler correctness for all input programs Compiler validation with formal methods involves a long chain of formal, deductive logic. However, since the tool to find the proof ( theorem prover) is implemented in software and is complex, there is a high probability it will contain errors. One approach has been to use a tool that verifies the proof (a proof checker) which, because it is much simpler than a proof-finder, is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, where the specification contains liveness requirements (such as avoidance of livelock) as well as safety requirements (such as avoidance of states representing a system crash). In order to solve such a problem algorithmically, both the model of the system and its specification are formulated in some precise mathematical language. To this end, the problem is formulated as a task in logic, namely to check whether a structure satisfies a given logical formula. This general concept applies to many kinds of logic and many kinds of structures. A simple model-checking problem consists of verifying whether a formula in the propositional logic is satisfied by a given structure. Overview Property checking is used for verification when two desc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Program Analysis
In computer science, program analysis is the process of automatically analyzing the behavior of computer programs regarding a property such as correctness, robustness, safety and liveness. Program analysis focuses on two major areas: program optimization and program correctness. The first focuses on improving the program’s performance while reducing the resource usage while the latter focuses on ensuring that the program does what it is supposed to do. Program analysis can be performed without executing the program (static program analysis), during runtime (dynamic program analysis) or in a combination of both. Static program analysis In the context of program correctness, static analysis can discover vulnerabilities during the development phase of the program.Jovanovic, N., Kruegel, C., & Kirda, E. (2006, May). Pixy: A static analysis tool for detecting web application vulnerabilities. In Security and Privacy, 2006 IEEE Symposium on (pp. 6-pp). IEEE. These vulnerabilities a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 methods of mathematics. Formal verification can be helpful in proving the correctness of systems such as: cryptographic protocols, combinational circuits, digital circuits with internal memory, and software expressed as source code. The verification of these systems is done by providing a formal proof on an abstract mathematical model of the system, the correspondence between the mathematical model and the nature of the system being otherwise known by construction. Examples of mathematical objects often used to model systems are: finite-state machines, labelled transition systems, Petri nets, vector addition systems, timed automata, hybrid automata, process algebra, formal semantics of programming languages such as operational semantics, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Testing
Software testing is the act of examining the artifacts and the behavior of the software under test by validation and verification. Software testing can also provide an objective, independent view of the software to allow the business to appreciate and understand the risks of software implementation. Test techniques include, but not necessarily limited to: * analyzing the product requirements for completeness and correctness in various contexts like industry perspective, business perspective, feasibility and viability of implementation, usability, performance, security, infrastructure considerations, etc. * reviewing the product architecture and the overall design of the product * working with product developers on improvement in coding techniques, design patterns, tests that can be written as part of code based on various techniques like boundary conditions, etc. * executing a program or application with the intent of examining behavior * reviewing the deployment infrastructure a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined abstraction, system of abstract thought. The term ''formalism'' is sometimes a rough synonym for ''formal system'', but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. Background Each formal system is described by primitive Symbol (formal), symbols (which collectively form an Alphabet (computer science), alphabet) to finitely construct a formal language from a set of axioms through inferential rules of formation. The system thus consists of valid formulas built up through finite combinations of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hoare Logic
Hoare logic (also known as Floyd–Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness of computer programs. It was proposed in 1969 by the British computer scientist and logician Tony Hoare, and subsequently refined by Hoare and other researchers. The original ideas were seeded by the work of Robert W. Floyd, who had published a similar system for flowcharts. Hoare triple The central feature of Hoare logic is the Hoare triple. A triple describes how the execution of a piece of code changes the state of the computation. A Hoare triple is of the form : \ C \ where P and Q are '' assertions'' and C is a ''command''.Hoare originally wrote "P\Q" rather than "\C\". P is named the ''precondition'' and Q the ''postcondition'': when the precondition is met, executing the command establishes the postcondition. Assertions are formulae in predicate logic. Hoare logic provides axioms and inference rules for all the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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