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Completeness and normal form of multi-valued logical functions

Journal of the Franklin Institute, 2020
Theory of completeness is essential for multi-valued logical functions. Using semi-tensor product (STP) of matrices, the algebraic form of k-valued logical functions is presented. Using algebraic form, a method is proposed to construct an adequate set of
D. Cheng, Zequn Liu, Hongsheng Qi
semanticscholar   +1 more source

Veritas: Deterministic Verilog Code Synthesis from LLM-Generated Conjunctive Normal Form

arXiv.org
Automated Verilog code synthesis poses significant challenges and typically demands expert oversight. Traditional high-level synthesis (HLS) methods often fail to scale for real-world designs. While large language models (LLMs) have enhanced scalability,
Prithwish Basu Roy   +6 more
semanticscholar   +1 more source

Short Conjunctive Normal Forms in Finitely Valued Logics

Journal of Logic and Computation, 1994
This paper deals with resolution theorem proving in many-valued logic. The latter has found increasing applications in such diverse fields as nonmonotonic reasoning, error-correcting codes, and software/hardware verification. Here, very long nonclausal formulae naturally come out, and efficient normal form reductions are, if not a \textit{sine qua non},
openaire   +1 more source

Conjunctive Normal Forms In Three-valued Propositional Logics

Journal of Logic and Computation, 1994
Summary: From a knowledge engineering point of view, and in spite of its formal virtues, conventional bi-valued propositional logics is, by its strict true/false dichotomy, severely limited in its conceptual expressivity. Thus a three-valued propositional calculus is proposed which offers more conceptual expressivity, without losing too much formal ...
openaire   +2 more sources

Variable Influences in Conjunctive Normal Forms

2009
We provide an upper bound on the total influence of Boolean functions defined by k -cnfs. Our bound is nearly optimal. We achieve it by an extension and appropriate use of an algorithm of Paturi, Pudlak, and Zane. We also discuss applications to prove and compute lower bounds for the maximum clause width k .
openaire   +1 more source

Knowledge representation by conjunctive normal forms and disjunctive normal forms based on n-variable-m-dimensional fundamental clauses and phrases

Fuzzy Sets and Systems, 1995
Abstract In this paper, the n-variable-m-dimensional fundamental phrases and clauses are used to completely build the universal basis for the general CNF and DNF. Furthermore, the general n-variable-m-dimensional CNF and DNF are also defined in order to construct the generally standard expressions of different axiom-based CNFs and DNFs such as 11 ...
Abraham Kandel   +2 more
openaire   +1 more source

Moving Between Conjunctive and Disjunctive Normal Forms

2018
As discussed in Chap. 1 (on inequality systems with logical connectives), disjunctive sets have many equivalent forms, of which the two extremes are the conjunctive normal form (CNF) and the disjunctive normal form (DNF). Although these two normal forms are at the opposite ends of the variety of equivalent forms, they share a property not common to all
openaire   +1 more source

Optimal Conjunctive Normal Form Encoding for Symbolic Execution

International Conferences on Software Engineering and Knowledge Engineering, 2021
Weiyu Pan, Ziqi Shuai, Ke Ma, Luyao Liu
openaire   +1 more source

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