Abstract
A NP hard problem CNF to DNF conversion is a vast area of research for AI, circuit design, FPGA’s (Miltersen et al. in On converting CNF To DNF, 2003), PLA’s, etc. (Beame in A switching lemma primer, 1994; Kottler and Kaufmann in SArTagnan—a parallel portfolio SAT solver with lockless physical clause sharing, 2011). Optimization and its statistics has become a potential requirement for analysis and behavior of normal form conversion. Various applications are in its requirement like gnome analysis, grid computing, bioinformatics, imaging systems, rough sets require higher variable processing algorithm. Problem statement is—design and implementation of optimal conjunctive normal form to optimal (prime implicants) disjunctive normal form conversion which is an “NP hard problem conversion to an NP complete”. Thus CNF to DNF can only be considered to evaluate best performance for higher variable processing on high end systems. The best-known representations of Boolean functions f are those as disjunctions of terms (DNFs) and as conjunctions of clauses (CNFs) (Beame 1994; Kottler and Kaufmann 2011) (Wegener in The complexity of boolean functions, 1987). It is convenient to define the DNF size of f as the minimal number of terms in a DNF representing f and the CNF size as the minimal number of clauses in a CNF representing f (Kottler and Kaufmann 2011).
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References
Beame P (1994) A switching lemma primer. University of Toronto
Kottler S, Kaufmann M (2011) SArTagnan—a parallel portfolio SAT solver with lockless physical clause sharing. University of Tuebingen, Tuebingen
Rosen KH (2003) Discrete mathematics and it’s applications, 6th edn, CRC Press, Boca Raton
Wegener I (1987) The complexity of boolean functions. Wiley and B.G.Teubner, Stuttgart
Auora R, Hsiao MS (2004) CNF formula simplification using implication reasoning. IEEE Transactions 0-7803-8714-7104 2004
Wahid Chrabakh, Rich Wolski (2003) GrADSAT: a parallel SAT solver for the grid. UCSB CS 2003-05, University of California
Biere A (2010) “Lingeling, Plingeling, PicoSAT and PrecoSAT”, FMV Reports Series, Aug 2010, Institute for Formal Models and Verification, Johannes Kepler University, Altenbergerstr. 69, 4040 Linz, Austria
Hamadi Y, Jabbour S (2009) ManySAT: a parallel SAT solver. J Satisf Boolean Model Comput 6:245–262
Fontoura M, Sadanandan S, Shanmugasundaram J, Vassilvitski S, Vee E, Venkatesan S, Zien J (2010) Efficiently evaluating complex boolean expressions, SIGMOD’10, 6–11 June 2010, Indianapolis, Indiana, USA
Miltersen PB, Radhakrishnan J Wegener I (2003) On converting CNF To DNF, Electronic Colloquium on Computational Complexity, Report No. 17, 2003
Zuim R, de Sousa JT, Coelho CN (2008) Decision heuristic for Davis Putnam, Loveland and Logemann algorithm satisfiability solving based on cube subtraction. IET Comput Digit Tech 2(1):30–39
Raut MK, Singh A (2004) Prime implicates of first order formulas. IITM Int J Comput Sci Appl 1:1–11
Nam G-J, Aloul F (2004) A comparative study of two boolean formulations of FPGA detailed routing constraints. IEEE Trans Comput 53(6):688–696
UCI Machine library for source input dataset (2012). http://archives.uci.com/machine
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Pardeshi, M.S. Recursive optimization on converting CNF to DNF using grid computing. CSIT 3, 23–29 (2015). https://doi.org/10.1007/s40012-015-0070-z
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DOI: https://doi.org/10.1007/s40012-015-0070-z