Representing a P-complete problem by small trellis automata
Alexander Okhotin
TL;DR
This paper introduces a new encoding of a P-complete problem and constructs a small trellis automaton with 11 states to solve it, demonstrating a compact automaton representation for P-complete problems.
Contribution
It presents a novel encoding of the Sequential NOR Circuit Value Problem and designs a minimal trellis automaton to solve it, advancing automaton-based representations of P-complete problems.
Findings
Trellis automaton with 11 states solves the problem
New encoding simplifies automaton construction
Demonstrates compact automaton for P-complete problem
Abstract
A restricted case of the Circuit Value Problem known as the Sequential NOR Circuit Value Problem was recently used to obtain very succinct examples of conjunctive grammars, Boolean grammars and language equations representing P-complete languages (Okhotin, http://dx.doi.org/10.1007/978-3-540-74593-8_23 "A simple P-complete problem and its representations by language equations", MCU 2007). In this paper, a new encoding of the same problem is proposed, and a trellis automaton (one-way real-time cellular automaton) with 11 states solving this problem is constructed.
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Taxonomy
TopicsDNA and Biological Computing · semigroups and automata theory · Cellular Automata and Applications