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A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can be used to represent a binary relation between a pair of finite sets. It is an important tool in combinatorial mathematics and theoretical computer science.
In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist. More formally, an undecidable problem is a problem whose language is not a recursive set ; see the article Decidable language .
In mathematics, a Boolean matrix is a matrix with entries from a Boolean algebra. When the two-element Boolean algebra is used, the Boolean matrix is called a logical matrix. (In some contexts, particularly computer science, the term "Boolean matrix" implies this restriction.) Let U be a non-trivial Boolean algebra (i.e. with at least two ...
Logic plays a fundamental role in computer science. Some of the key areas of logic that are particularly significant are computability theory (formerly called recursion theory), modal logic and category theory. The theory of computation is based on concepts defined by logicians and mathematicians such as Alonzo Church and Alan Turing.
The Boolean satisfiability problem (SAT) is, given a formula, to check whether it is satisfiable. This decision problem is of central importance in many areas of computer science, including theoretical computer science, complexity theory, [3] [4] algorithmics, cryptography [5] [6] and artificial intelligence. [7] [additional citation(s) needed]
The Circuit Value Problem — the problem of computing the output of a given Boolean circuit on a given input string — is a P-complete decision problem. [3]: 119 Therefore, this problem is considered to be "inherently sequential" in the sense that there is likely no efficient, highly parallel algorithm that solves the problem.
This is a list of mathematical logic topics. For traditional syllogistic logic, see the list of topics in logic . See also the list of computability and complexity topics for more theory of algorithms .
This article is a list of notable unsolved problems in computer science. A problem in computer science is considered unsolved when no solution is known or when experts in the field disagree about proposed solutions.