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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Bibliographic Details
Published in:Information sciences Vol. 85; no. 1; pp. 175 - 184
Main Authors: Pradeep, B., Siva Ram Murthy, C.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.07.1995
Elsevier Science
Subjects:
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
Online Access:Get full text
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Summary: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.
ISSN:0020-0255
1872-6291
DOI:10.1016/0020-0255(95)00026-L