Polynomial Time Identification of Strict Deterministic Restricted One-Counter Automata in Some Class from Positive Data

Abstract

A deterministic pushdown automaton (dpda) having just one stack symbol is called a deterministic restricted one-counter automaton (droca). When it accepts by empty stack, it is called strict. This paper is concerned with a subclass of real-time strict droca’s called Szilard strict droca’s. The class of languages accepted by Szilard strict droca’s is incomparable to both the class of regular languages and that of simple languages. We show that the class of Szilard strict droca’s is polynomial time identifiable in the limit from positive data in the sense of Yokomori. This identifiability is proved by giving an exact characteristic sample of polynomial size for a language accepted by a Szilard strict droca. The class of very simple languages is also proved to be polynomial time identifiable in the limit from positive data by Yokomori, but it is still unknown whether there exists a characteristic sample of polynomial size for any very simple language.

This work has been supported in part by Grant-in-Aid for Scientific Research Nos. 13680435 and 16300001 from the Ministry of Education, Culture, Sports, Science and Technology of Japan.