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CVC4
In computer science and mathematical logic, Cooperating Validity Checker (CVC) is a family of satisfiability modulo theories (SMT) solvers. The latest major versions of CVC are CVC4 and CVC5 (stylized cvc5); earlier versions include CVC, CVC Lite, and CVC3. Both CVC4 and cvc5 support the SMT-LIB and TPTP input formats for solving SMT problems, and the SyGuS-IF format for program synthesis. Both CVC4 and cvc5 can output proofs that can be independently checked in the LFSC format, cvc5 additionally supports the Alethe and Lean 4 formats. cvc5 has bindings for C++, Python, and Java. CVC4 competed in SMT-COMP in the years 2014-2020, and cvc5 has competed in the years 2021-2022. CVC4 competed in SyGuS-COMP in the years 2015-2019, and in CASC in 2013-2015. CVC4 uses the DPLL(T) architecture, and supports the theories of linear arithmetic over rationals and integers, fixed-width bitvectors, floating-point arithmetic, strings, (co)-datatypes, sequences (used to model dynamic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Satisfiability Modulo Theories
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable. It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings. The name is derived from the fact that these expressions are interpreted within ("modulo") a certain formal theory in first-order logic with equality (often disallowing quantifiers). SMT solvers are tools that aim to solve the SMT problem for a practical subset of inputs. SMT solvers such as Z3 and cvc5 have been used as a building block for a wide range of applications across computer science, including in automated theorem proving, program analysis, program verification, and software testing. Since Boolean satisfiability is already NP-complete, the SMT problem is typically NP-hard, and for many theories it is undecidable. Re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DPLL(T)
In computer science, DPLL(T) is a framework for determining the satisfiability of SMT problems. The algorithm extends the original SAT-solving DPLL algorithm with the ability to reason about an arbitrary theory ''T''. At a high level, the algorithm works by transforming an SMT problem into a SAT formula where atoms are replaced with Boolean variables. The algorithm repeatedly finds a satisfying valuation for the SAT problem, consults a theory solver to check consistency under the domain-specific theory, and then (if a contradiction is found) refines the SAT formula with this information. Many modern SMT solvers, such as Microsoft's Z3 Theorem Prover and CVC4 In computer science and mathematical logic, Cooperating Validity Checker (CVC) is a family of satisfiability modulo theories (SMT) solvers. The latest major versions of CVC are CVC4 and CVC5 (stylized cvc5); earlier versions include CVC, CVC Li ..., use DPLL(T) to power their core solving capabilities. References A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanford University
Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth List of governors of California, governor of and then-incumbent List of United States senators from California, United States senator representing California) and his wife, Jane Stanford, Jane, in memory of their only child, Leland Stanford Jr., Leland Jr. The university admitted its first students in 1891, opening as a Mixed-sex education, coeducational and non-denominational institution. It struggled financially after Leland died in 1893 and again after much of the campus was damaged by the 1906 San Francisco earthquake. Following World War II, university Provost (education), provost Frederick Terman inspired an entrepreneurship, entrepreneurial culture to build a self-sufficient local industry (later Silicon Valley). In 1951, Stanfor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (for example, The set of all rational numbers is often referred to as "the rationals", and is closed under addition, subtraction, multiplication, and division by a nonzero rational number. It is a field under these operations and therefore also called the field of rationals or the field of rational numbers. It is usually denoted by boldface , or blackboard bold A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example: ), or eventually begins to repeat the same finite sequence of digits over and over (example: ). This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones (see ). A real n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set (mathematics), set of all integers is often denoted by the boldface or blackboard bold The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the set of natural numbers, the set of integers \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , 5/4, and Square root of 2, are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating-point Arithmetic
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a Sign (mathematics), signed sequence of a fixed number of digits in some Radix, base) multiplied by an integer power of that base. Numbers of this form are called floating-point numbers. For example, the number 2469/200 is a floating-point number in base ten with five digits: 2469/200 = 12.345 = \! \underbrace_\text \! \times \! \underbrace_\text\!\!\!\!\!\!\!\overbrace^ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits. The nearest floating-point number with only five digits is 12.346. And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits. In practice, most floating-point systems use Binary number, base two, though base ten (decimal floating point) is also common. Floating-point arithmetic operations, such as addition and division, approximate the correspond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String (computer Science)
In computer programming, a string is traditionally a sequence of character (computing), characters, either as a literal (computer programming), literal constant or as some kind of Variable (computer science), variable. The latter may allow its elements to be Immutable object, mutated and the length changed, or it may be fixed (after creation). A string is often implemented as an array data structure of bytes (or word (computer architecture), words) that stores a sequence of elements, typically characters, using some character encoding. More general, ''string'' may also denote a sequence (or List (abstract data type), list) of data other than just characters. Depending on the programming language and precise data type used, a variable (programming), variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears lit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Type
In computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. A data type specification in a program constrains the possible values that an expression, such as a variable or a function call, might take. On literal data, it tells the compiler or interpreter how the programmer intends to use the data. Most programming languages support basic data types of integer numbers (of varying sizes), floating-point numbers (which approximate real numbers), characters and Booleans. Concept A data type may be specified for many reasons: similarity, convenience, or to focus the attention. It is frequently a matter of good organization that aids the understanding of complex definitions. Almost all programming languages explicitly include the notion of data type, though the possible d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter "M" first and "Y" last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be '' finite'', as in these examples, or '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Array
In computer science, a dynamic array, growable array, resizable array, dynamic table, mutable array, or array list is a random access, variable-size list data structure that allows elements to be added or removed. It is supplied with standard libraries in many modern mainstream programming languages. Dynamic arrays overcome a limit of static arrays, which have a fixed capacity that needs to be specified at allocation. A dynamic array is not the same thing as a dynamically allocated array or variable-length array, either of which is an array whose size is fixed when the array is allocated, although a dynamic array may use such a fixed-size array as a back end.See, for example, thsource code of java.util.ArrayList class from OpenJDK 6 Bounded-size dynamic arrays and capacity A simple dynamic array can be constructed by allocating an array of fixed-size, typically larger than the number of elements immediately required. The elements of the dynamic array are stored contiguous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
