l-Valued multiset automata and l-valued multiset languages

The reason for this work is to present and study deterministic multiset automata, multiset automata and their languages with membership values in complete residuated lattice without zero divisors. We build up the comparability of deterministic [Formula: see text]-valued multiset finite automaton and [Formula: see text]-valued multiset finite automaton in sense of recognizability of a [Formula: see text]-valued multiset language. Then, we relate multiset regular languages to a given [Formula: see text]-valued multiset regular languages and vice versa. At last, we present the concept of pumping lemma for [Formula: see text]-valued multiset automata theory, which we utilize to give a necessary and sufficient condition for a [Formula: see text]-valued multiset language to be non-constant.

Fuzzy Regular Languages Based on Residuated Lattice

The purpose of this work is to introduce the concept of fuzzy regular languages (FRL) accepted by fuzzy finite automata, and try to introduce the categorical look of fuzzy languages where the codomain of membership functions are taken as a complete residuated lattice, instead of [Formula: see text]. Also, we have introduced pumping lemma for FRL, which is used to establish a necessary and sufficient condition for a given fuzzy languages to be non-constant.

A Pumping Lemma for Permitting Semi-Conditional Languages

Permitting semi-conditional grammars (pSCGs) are extensions of context-free grammars where each rule is associated with a word [Formula: see text] and such a rule can be applied to a sentential form [Formula: see text] only if [Formula: see text] is a subword of [Formula: see text]. We consider permitting generalized SCGs (pgSCGs) where each rule [Formula: see text] is associated with a set of words [Formula: see text] and [Formula: see text] is applicable only if every word in [Formula: see text] occurs in [Formula: see text]. We investigate the generative power of pgSCGs with no erasing rules and prove a pumping lemma for their languages. Using this lemma we show that pgSCGs are strictly weaker than context-sensitive grammars. This solves a long-lasting open problem concerning the generative power of pSCGs. Moreover, we give a comparison of the generating power of pgSCGs and that of forbidding random context grammars with no erasing rules.

One-Way Jumping Finite Automata

We propose the one-way jumping finite automaton model, restricting the jumping relation of the recently introduced jumping finite automaton so that the machine can only jump over symbols it cannot process in its current state. The reading head of a one-way jumping finite automaton moves deterministically in one direction within the input word, whereas movement of the reading head of jumping finite automaton is non-deterministic. The class of languages accepted by one-way jumping finite automata is different from that of jumping finite automata, in particular, it includes all regular languages, as opposed to the latter. We study one-way jumping finite automata and obtain closure properties, a pumping lemma, and separation results with respect to the classical language classes of the Chomsky hierarchy.