A constant time algorithm for theorem proving in propositional logic on reconfigurable meshes

In this paper, we present an O(1) time algorithm for theorem proving in propositional logic on processor arrays with a reconfigurable bus system of size m × 2 n , where m is the number of clauses and n is the number of Boolean variables. The theorem proving problem involves combinatorial exploration...

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Vydáno v:	Information sciences Ročník 85; číslo 1; s. 175 - 184
Hlavní autoři:	Pradeep, B., Siva Ram Murthy, C.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY Elsevier Inc 01.07.1995 Elsevier Science
Témata:	Algorithmics. Computability. Computer arithmetics Applied sciences Artificial intelligence Computer science; control theory; systems Exact sciences and technology Learning and adaptive systems Programming theory Theoretical computing Propositional logic Parallel algorithm Array processor Theorem proving Combinatorial problem Logic array Time complexity Inference rule Reconfiguration Bus system
ISSN:	0020-0255, 1872-6291
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Abstract	In this paper, we present an O(1) time algorithm for theorem proving in propositional logic on processor arrays with a reconfigurable bus system of size m × 2 n , where m is the number of clauses and n is the number of Boolean variables. The theorem proving problem involves combinatorial exploration of an exponential search space. Our approach to the problem is simpler than using explicit inference rules, as the problem is vectorized and deductions are performed implicitly by simple AND and OR oprrations on vectors. The previous best parallel algorithm for the theorem proving problem available in the literature has a time complexity of O( m log 2 n) using O(2 n ) processors. Thus, our algorithm is faster and further; costwise (time complexity × number of processors), it is efficient by a factor of log 2 n.
AbstractList	In this paper, we present an O(1) time algorithm for theorem proving in propositional logic on processor arrays with a reconfigurable bus system of size m × 2 n , where m is the number of clauses and n is the number of Boolean variables. The theorem proving problem involves combinatorial exploration of an exponential search space. Our approach to the problem is simpler than using explicit inference rules, as the problem is vectorized and deductions are performed implicitly by simple AND and OR oprrations on vectors. The previous best parallel algorithm for the theorem proving problem available in the literature has a time complexity of O( m log 2 n) using O(2 n ) processors. Thus, our algorithm is faster and further; costwise (time complexity × number of processors), it is efficient by a factor of log 2 n.
Author	Pradeep, B. Siva Ram Murthy, C.
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Keywords	Propositional logic Parallel algorithm Array processor Theorem proving Combinatorial problem Logic array Time complexity Inference rule Reconfiguration Bus system
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SubjectTerms	Algorithmics. Computability. Computer arithmetics Applied sciences Artificial intelligence Computer science; control theory; systems Exact sciences and technology Learning and adaptive systems Programming theory Theoretical computing
Title	A constant time algorithm for theorem proving in propositional logic on reconfigurable meshes
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