A simple P-complete problem and its representations by language equations

Authors:
Alexander Okhotin
Affiliations:
Academy of Finland and Department of Mathematics, University of Turku, Turku, Finland
Venue:
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Year:
2007

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Abstract

A variant of Circuit Value Problem over the basis of Peirce's arrow (NOR) is introduced, in which one of the inputs of every k-th 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. It is shown that this language can be naturally and succinctly represented by language equations from several classes. Using this representation, a small conjunctive grammar and an even smaller LL(1) Boolean grammar for this language are constructed.