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Proof Of 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: 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 partia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science
Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The Association for Computing Machinery, ACM's 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 Mathematical Theory of Communication, 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 neural networks and para ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Theory
Proof theory is a major branchAccording to , proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. consists of four corresponding parts, with part D being about "Proof Theory and Constructive Mathematics". of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research also ... [...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 symbolic 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 ... [...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, ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Program Analysis
In computer science, program analysis is the process of 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 are easier t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Design By Contract
Design by contract (DbC), also known as contract programming, programming by contract and design-by-contract programming, is an approach for designing software. It prescribes that software designers should define formal, precise and verifiable interface specifications for software components, which extend the ordinary definition of abstract data types with preconditions, postconditions and invariants. These specifications are referred to as "contracts", in accordance with a conceptual metaphor with the conditions and obligations of business contracts. The DbC approach assumes all ''client components'' that invoke an operation on a ''server component'' will meet the preconditions specified as required for that operation. Where this assumption is considered too risky (as in multi-channel or distributed computing), the inverse approach is taken, meaning that the ''server component'' tests that all relevant preconditions hold true (before, or while, processing the ''client co ... [...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 a system with respect to a certain formal specification or property, using formal methods of mathematics. Formal verification is a key incentive for formal specification of systems, and is at the core of formal methods. It represents an important dimension of analysis and verification in electronic design automation and is one approach to software verification. The use of formal verification enables the highest Evaluation Assurance Level ( EAL7) in the framework of common criteria for computer security certification. 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 in a programming language. Prominent examples of verified software systems include the CompCert verified C compiler and the seL ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Testing
Software testing is the act of checking whether software satisfies expectations. Software testing can provide objective, independent information about the Quality (business), quality of software and the risk of its failure to a User (computing), user or sponsor. Software testing can determine the Correctness (computer science), correctness of software for specific Scenario (computing), scenarios but cannot determine correctness for all scenarios. It cannot find all software bug, bugs. Based on the criteria for measuring correctness from an test oracle, oracle, software testing employs principles and mechanisms that might recognize a problem. Examples of oracles include specifications, Design by Contract, contracts, comparable products, past versions of the same product, inferences about intended or expected purpose, user or customer expectations, relevant standards, and applicable laws. Software testing is often dynamic in nature; running the software to verify actual output ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal System
A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in mathematics. 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. Concepts A formal system has the following: * Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules). * Deductive system, deductive apparatus, or proof system, which has rules of inference that take axioms and infers theorems, both of which are part of the formal language. A formal system is said to be recursive (i.e. effective) or recursively enumerable if the set of axioms and the set of inference rules are decidable ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
