A1 Refereed original research article in a scientific journal
A simple P-complete problem and its language-theoretic representations
Authors: Okhotin A
Publisher: ELSEVIER SCIENCE BV
Publication year: 2011
Journal: Theoretical Computer Science
Journal name in source: THEORETICAL COMPUTER SCIENCE
Journal acronym: THEOR COMPUT SCI
Number in series: 1-2
Volume: 412
Issue: 1-2
First page : 68
Last page: 82
Number of pages: 15
ISSN: 0304-3975
DOI: https://doi.org/10.1016/j.tcs.2010.09.015
Abstract
A variant of the Circuit Value Problem is introduced, in which every gate implements the NOR function -(x v y), and one of the inputs of every kth gate must be the (k - 1)th gate. The problem, which remains P-complete, is encoded as a simple formal language over a two-letter alphabet, which can be succinctly represented by language equations of several types. Using this representation, a conjunctive grammar with 8 rules, a Boolean grammar with 5 rules and an LL(1) Boolean grammar with 8 rules for this language are constructed. Another encoding of the problem is represented by a trellis automaton with 11 states and a linear conjunctive grammar with 20 rules. (C) 2010 Elsevier B.V. All rights reserved.
A variant of the Circuit Value Problem is introduced, in which every gate implements the NOR function -(x v y), and one of the inputs of every kth gate must be the (k - 1)th gate. The problem, which remains P-complete, is encoded as a simple formal language over a two-letter alphabet, which can be succinctly represented by language equations of several types. Using this representation, a conjunctive grammar with 8 rules, a Boolean grammar with 5 rules and an LL(1) Boolean grammar with 8 rules for this language are constructed. Another encoding of the problem is represented by a trellis automaton with 11 states and a linear conjunctive grammar with 20 rules. (C) 2010 Elsevier B.V. All rights reserved.
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