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A satisfiability tester for nonclausal propositional calculus
 Information and Computation
, 1988
"... An algorithm for satisfiability testing in the propositional calculus with a worst case running time that grows at a rate less than 2 (.25+ε) L is described, where L can be either the length of the input expression or the number of occurrences of literals (i.e., leaves) in it. This represents a new ..."
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An algorithm for satisfiability testing in the propositional calculus with a worst case running time that grows at a rate less than 2 (.25+ε) L is described, where L can be either the length of the input expression or the number of occurrences of literals (i.e., leaves) in it. This represents a new upper bound on the complexity of nonclausal satisfiability testing. The performance is achieved by using lemmas concerning assignments and pruning that preserve satisfiability, together with choosing a &quot;good &quot; variable upon which to recur. For expressions in conjunctive normal form, it is shown that an upper bound is 2.128 L.
The Complexity of Automated Reasoning
, 1989
"... This thesis explores the relative complexity of proofs produced by the automatic theorem proving procedures of analytic tableaux, linear resolution, the connection method, tree resolution and the DavisPutnam procedure. It is shown that tree resolution simulates the improved tableau procedure and th ..."
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This thesis explores the relative complexity of proofs produced by the automatic theorem proving procedures of analytic tableaux, linear resolution, the connection method, tree resolution and the DavisPutnam procedure. It is shown that tree resolution simulates the improved tableau procedure and that SLresolution and the connection method are equivalent to restrictions of the improved tableau method. The theorem by Tseitin that the DavisPutnam Procedure cannot be simulated by tree resolution is given an explicit and simplified proof. The hard examples for tree resolution are contradictions constructed from simple Tseitin graphs.
NANOTECHNOLOGY
, 2008
"... doi:10.1088/09574484/19/39/395103 The use of gold nanoparticle aggregation for DNA computing and logicbased biomolecular detection ..."
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doi:10.1088/09574484/19/39/395103 The use of gold nanoparticle aggregation for DNA computing and logicbased biomolecular detection
1 A Satisfiability Tester for NonClausal Propositional Calculus
"... AbstractAn algorithm for satisfiability testing in the propositional calculus with a worst case running time that grows at a rate less than 2 (.25+e) L is described, where L can be either the length of theinput expression or the number of occurrences of literals (i.e., leaves) in it. This represents ..."
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AbstractAn algorithm for satisfiability testing in the propositional calculus with a worst case running time that grows at a rate less than 2 (.25+e) L is described, where L can be either the length of theinput expression or the number of occurrences of literals (i.e., leaves) in it. This represents a new upper bound on the complexity of nonclausal satisfiability testing. The performance isachieved by using lemmas concerning assignments and pruning that preserve satisfiability, together with choosing a "good " variable upon which to recur. For expressions in conjunctivenormal form, it is shown that an upper bound is 2.128 L.
On Conjunctive Normal Form Satisfiability
, 1991
"... This paper focuses on algorithms that solve CSAT (conjunctive normal form satisfiability) by searching for a satisfying truth assignment for the given formula F. We identify four basic ways to improve the basic search procedure: constraint propagators, simplifying transformations, heuristics, and ot ..."
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This paper focuses on algorithms that solve CSAT (conjunctive normal form satisfiability) by searching for a satisfying truth assignment for the given formula F. We identify four basic ways to improve the basic search procedure: constraint propagators, simplifying transformations, heuristics, and other miscellaneous improvements. In each of these categories, we survey the existing improvements and suggest new ones. We lower the average time it takes to perform the simplest kind of constraint propagation from O(L) to O(L/P), where L is the length of F and P is the number of propositions in F; this is optimal. We lower the current upper bound for CSAT from O(20.128 L) to O(20.128 (LN)), where N is the number of clauses in F. Finally, we experimentally determine the fastest possible algorithm with respect to each of the basic improvements we consider.