APCol Systems with Verifier Agents

Abstract

APCol systems (Automaton-like P colonies) are variants of P colonies where the environment is given by a string and the agents change their own states and the environmental string similarly to automata. By the original definition, the input (initial environmental) string is accepted if it can be reduced to the empty word. In this paper, we continue the examination of a variant of APCol systems where the agents explore and verify their common environment (the notion was introduced as verifying APCol systems). In this case, an input string of length n is accepted if there is a halting computation c such that the length of the environmental strings remains unchanged during the computation and for every agent and for each position each i, $1\le i\le n$, there is an environmental string obtained by c such that the agent applies a rule to position i. Improving a previous result, we show that APCol systems with verifier agents simulate nondeterministic two-way multihead automata. The result implies that any language in $\text {NSPACE}(\log n)$can be accepted by an APCol system with verifier agents.