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Automated theorem proving is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science.
Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics".
In computer science, static program analysis is the analysis of computer programs performed without executing them, in contrast with dynamic program analysis, which is performed on programs during their execution.
In computer science, formal methods are mathematically rigorous techniques for the specification, development, analysis, and verification of software 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.
The Isabelle automated theorem prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala. As an LCF-style theorem prover, it is based on a small logical core (kernel) to increase the trustworthiness of proofs without requiring — yet supporting — explicit proof objects.
ACL2 is a software system consisting of a programming language, an extensible theory in a first-order logic, and an automated theorem prover. ACL2 is designed to support automated reasoning in inductive logical theories, mostly for software and hardware verification. The input language and implementation of ACL2 are written in Common Lisp. ACL2 is free and open-source software.
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.
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. This is typically associated with hardware or software systems, where the specification contains liveness requirements as well as safety requirements.
A race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is dependent on the sequence or timing of other uncontrollable events. It becomes a bug when one or more of the possible behaviors is undesirable.
In logic and mathematics, a formal proof or derivation is a finite sequence of sentences, each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically verifiable. If the set of assumptions is empty, then the last sentence in a formal proof is called a theorem of the formal system. The notion of theorem is not in general effective, therefore there may be no method by which we can always find a proof of a given sentence or determine that none exists. The concepts of Fitch-style proof, sequent calculus and natural deduction are generalizations of the concept of proof.
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer.
In computer science, in particular in knowledge representation and reasoning and metalogic, the area of automated reasoning is dedicated to understanding different aspects of reasoning. The study of automated reasoning helps produce computer programs that allow computers to reason completely, or nearly completely, automatically. Although automated reasoning is considered a sub-field of artificial intelligence, it also has connections with theoretical computer science and philosophy.
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 which 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.
The KeY tool is used in formal verification of Java programs. It accepts specifications written in the Java Modeling Language to Java source files. These are transformed into theorems of dynamic logic and then compared against program semantics that are likewise defined in terms of dynamic logic. KeY is significantly powerful in that it supports both interactive and fully automated correctness proofs. Failed proof attempts can be used for a more efficient debugging or verification-based testing. There have been several extensions to KeY in order to apply it to the verification of C programs or hybrid systems. KeY is jointly developed by Karlsruhe Institute of Technology, Germany; Technische Universität Darmstadt, Germany; and Chalmers University of Technology in Gothenburg, Sweden and is licensed under the GPL.
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 on an existing compiler.
Concolic testing is a hybrid software verification technique that performs symbolic execution, a classical technique that treats program variables as symbolic variables, along a concrete execution path. Symbolic execution is used in conjunction with an automated theorem prover or constraint solver based on constraint logic programming to generate new concrete inputs with the aim of maximizing code coverage. Its main focus is finding bugs in real-world software, rather than demonstrating program correctness.
In information technology a reasoning system is a software system that generates conclusions from available knowledge using logical techniques such as deduction and induction. Reasoning systems play an important role in the implementation of artificial intelligence and knowledge-based systems.
Dafny is an imperative and functional compiled language that compiles to other programming languages, such as C#, Java, JavaScript, Go and Python. It supports formal specification through preconditions, postconditions, loop invariants, loop variants, termination specifications and read/write framing specifications. The language combines ideas from the functional and imperative paradigms; it includes support for object-oriented programming. Features include generic classes, dynamic allocation, inductive datatypes and a variation of separation logic known as implicit dynamic frames for reasoning about side effects. Dafny was created by Rustan Leino at Microsoft Research after his previous work on developing ESC/Modula-3, ESC/Java, and Spec#.
Grigore Roșu is a computer science professor at the University of Illinois at Urbana-Champaign and a researcher in the Information Trust Institute. He is known for his contributions in runtime verification, the K framework, matching logic, and automated coinduction.
Z3, also known as the Z3 Theorem Prover, is a satisfiability modulo theories (SMT) solver developed by Microsoft.
References
- ↑ John Matthews; J. Strother Moore; Sandip Ray; Daron Vroon (2005). "Verification Condition Generation Via Theorem Proving". In Miki Hermann; Andrei Voronkov (eds.). Proc. Int. Conf. Logic for Programming, Artificial Intelligence, and Reasoning . LNCS. Vol. 4246. Springer. pp. 362–376.
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