A simple P-complete problem and its language-theoretic representations
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.
circuit value problem language equations conjunctive grammars boolean grammars trellis automata