Mathematical Foundation of a Functional Implementation of the CNF Algorithm

The conjunctive normal form (CNF) algorithm is one of the best known and most widely used algorithms in classical logic and its applications. In its algebraic approach, it makes use in a loop of a certain well-defined operation related to the “distributivity” of logical disjunction versus conjunctio...

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Vydáno v:Algorithms Ročník 16; číslo 10; s. 459
Hlavní autoři: García-Olmedo, Francisco Miguel, García-Miranda, Jesús, González-Rodelas, Pedro
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.10.2023
Témata:
Algorithms
Associativity
Boolean
Boolean algebra
Canonical forms
classical logic
CNF
Horn clauses
Iterative methods
Language
Logic
Mathematical analysis
reverse engineering
SAT problem
Semantics
Germany
ISSN:1999-4893, 1999-4893
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Shrnutí:The conjunctive normal form (CNF) algorithm is one of the best known and most widely used algorithms in classical logic and its applications. In its algebraic approach, it makes use in a loop of a certain well-defined operation related to the “distributivity” of logical disjunction versus conjunction. For those types of implementations, the loop iteration runs a comparison between formulas to decide when to stop. In this article, we explain how to pre-calculate the exact number of loop iterations, thus avoiding the work involved in the above-mentioned comparison. After that, it is possible to concatenate another loop focused now on the “associativity” of conjunction and disjunction. Also for that loop, we explain how to calculate the optimal number of rounds, so that the decisional comparison phase for stopping can be also avoided.
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ISSN:1999-4893
1999-4893
DOI:10.3390/a16100459