 | This article is missing information about if they are named after somebody? When were they first defined? Perhaps add an example?.(December 2023) |
Constrained Horn clauses (CHCs) are a fragment of first-order logic with applications to program verification and synthesis. Constrained Horn clauses can be seen as a form of constraint logic programming. [1]
A constrained Horn clause is a formula of the form
where is a constraint in some first-order theory, are predicates, and are universally-quantified variables.
The satisfiability of constrained Horn clauses with constraints from linear integer arithmetic is undecidable. [2]
There are several automated solvers for CHCs, [3] including the SPACER engine of Z3. [4]
CHC-COMP is an annual competition of CHC solvers. [5] CHC-COMP has run every year since 2018.
Constrained Horn clauses are a convenient language in which to specify problems in program verification. [6] The SeaHorn verifier for LLVM represents verification conditions as constrained Horn clauses, [7] as does the JayHorn verifier for Java. [8]
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called satisfiable. On the other hand, if no such assignment exists, the function expressed by the formula is FALSE for all possible variable assignments and the formula is unsatisfiable. For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make (a AND NOT b) = TRUE. In contrast, "a AND NOT a" is unsatisfiable.
Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical form, representing knowledge about some problem domain. Computation is performed by applying logical reasoning to that knowledge, to solve problems in the domain. Major logic programming language families include Prolog, Answer Set Programming (ASP) and Datalog. In all of these languages, rules are written in the form of clauses:
Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize a multivariate quadratic function subject to linear constraints on the variables. Quadratic programming is a type of nonlinear programming.
Inductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples, background knowledge and hypotheses. The term "inductive" here refers to philosophical rather than mathematical induction. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesised logic program which entails all the positive and none of the negative examples.
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An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints are linear.
In computer science, 2-satisfiability, 2-SAT or just 2SAT is a computational problem of assigning values to variables, each of which has two possible values, in order to satisfy a system of constraints on pairs of variables. It is a special case of the general Boolean satisfiability problem, which can involve constraints on more than two variables, and of constraint satisfaction problems, which can allow more than two choices for the value of each variable. But in contrast to those more general problems, which are NP-complete, 2-satisfiability can be solved in polynomial time.
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Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets. Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
In constrained optimization, a field of mathematics, a barrier function is a continuous function whose value increases to infinity as its argument approaches the boundary of the feasible region of an optimization problem. Such functions are used to replace inequality constraints by a penalizing term in the objective function that is easier to handle. A barrier function is also called an interior penalty function, as it is a penalty function that forces the solution to remain within the interior of the feasible region.
In computer science, separation logic is an extension of Hoare logic, a way of reasoning about programs. It was developed by John C. Reynolds, Peter O'Hearn, Samin Ishtiaq and Hongseok Yang, drawing upon early work by Rod Burstall. The assertion language of separation logic is a special case of the logic of bunched implications (BI). A CACM review article by O'Hearn charts developments in the subject to early 2019.
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. 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.
In computer science, the International Conference on Computer-Aided Verification (CAV) is an annual academic conference on the theory and practice of computer-aided formal analysis of software and hardware systems, broadly known as formal methods. Among the important results originally published in CAV are techniques in model checking, such as Counterexample-Guided Abstraction Refinement (CEGAR) and partial order reduction. It is often ranked among the top conferences in computer science.
In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem. On input a formula over Boolean variables, such as "(x or y) and (x or not y)", a SAT solver outputs whether the formula is satisfiable, meaning that there are possible values of x and y which make the formula true, or unsatisfiable, meaning that there are no such values of x and y. In this case, the formula is satisfiable when x is true, so the solver should return "satisfiable". Since the introduction of algorithms for SAT in the 1960s, modern SAT solvers have grown into complex software artifacts involving a large number of heuristics and program optimizations to work efficiently.
In mathematical optimization, the problem of non-negative least squares (NNLS) is a type of constrained least squares problem where the coefficients are not allowed to become negative. That is, given a matrix A and a (column) vector of response variables y, the goal is to find
In computer science, hyperproperties are a formalism for describing properties of computational systems. Hyperproperties generalize safety and liveness properties, and can express properties such as non-interference and observational determinism.
Kenneth L. McMillan is an American computer scientist working in the area of formal methods, logic, and programming languages. He is a professor in the computer science department at the University of Texas at Austin, where he holds the Admiral B.R. Inman Centennial Chair in Computing Theory.
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 ; 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.
Counterexample-guided abstraction refinement (CEGAR) is a technique for symbolic model checking. It is also applied in modal logic tableau calculi algorithms to optimise their efficiency.
Modal clausal form, also known as separated normal form by modal levels (SNFml) and Mints normal form, is a normal form for modal logic formulae.
CHCs are syntactically and semantically the same as constraint logic programs
