Showing papers by "Tomáš Masopust published in 2009"

Cooperating Distributed Grammar Systems with PermittingGrammars as Components

Abstract: This paper studies cooperating distributed grammar systems working in the terminal derivation mode where the components are variants of permitting grammars. It proves that although the family of permitting languages is strictly included in the family of random context languages, the families of random context languages and languages generated by permitting cooperating distributed grammar systems in the above mentioned derivation mode coincide. Moreover, if the components are so-called left-permitting grammars, then cooperating distributed grammar systems in the terminal mode characterize the class of context-sensitive languages, or if erasing rules are allowed, the class of recursively enumerable languages. Descriptional complexity results are also presented. It is shown that the number of permitting components can be bounded, in the case of left-permitting components with erasing rules even together with the number of nonterminals.

On the terminating derivation mode in cooperating distributed grammar systems with forbidding components

Abstract: This paper discusses the terminating derivation mode in cooperating distributed grammar systems where components are forbidding grammars instead of context-free grammars. Such systems are called forbidding cooperating distributed grammar systems, and it is demonstrated that the number of their components can be reduced to two without changing the generative power and that these systems are computationally complete. Without erasing productions, however, these systems are less powerful than context-sensitive grammars.

Cooperating distributed grammar systems with permitting grammars as components

Abstract: This paper studies cooperating distributed grammar systems working in the terminal derivation mode where the components are variants of permitting grammars. It proves that although the family of permitting languages is strictly included in the family of random context languages, the families of random context languages and languages generated by permitting cooperating distributed grammar systems in the above mentioned derivation mode coincide. Moreover, if the components are so-called left-permitting grammars, then cooperating distributed grammar systems in the terminal mode characterize the class of context-sensitive languages, or if erasing rules are allowed, the class of recursively enumerable languages. Descriptional complexity results are also presented. It is shown that the number of permitting components can be bounded, in the case of left-permitting components with erasing rules even together with the number of nonterminals.

A Note on the Generative Power of Some Simple Variants of Context-Free Grammars Regulated by Context Conditions

Abstract: This paper answers three open questions concerning the generative power of some simple variants of context-free grammars regulated by context conditions. Specifically, it discusses the generative power of so-called context-free semi-conditional grammars (which are random context grammars where permitting and forbidding sets are replaced with permitting and forbidding strings) where permitting and forbidding strings of each production are of length no more than one, and of simple semi-conditional grammars where, in addition, no production has attached both a permitting and a forbidding string. Finally, this paper also presents some normal form results, an overview of known results, and unsolved problems.

Descriptional Complexity of Three-Nonterminal Scattered Context Grammars: An Improvement

Abstract: Recently, it has been shown that every recursively enumerable language can be generated by a scattered context grammar with no more than three nonterminals. However, in that construction, the maximal number of nonterminals simultaneously rewritten during a derivation step depends on many factors, such as the cardinality of the alphabet of the generated language and the structure of the generated language itself. This paper improves the result by showing that the maximal number of nonterminals simultaneously rewritten during any derivation step can be limited by a small constant regardless of other factors.

Descriptional Complexity of Three-Nonterminal Scattered Context Grammars: An Improvement

Abstract: z Abstract. Recently, it has been shown that every recursively enumer- able language can be generated by a scattered context grammar with no more than three nonterminals. However, in that construction, the maxi- mal number of nonterminals simultaneously rewritten during a derivation step depends on many factors, such as the cardinality of the alphabet of the generated language and the structure of the generated language itself. This paper improves the result by showing that the maximal number of nonterminals simultaneously rewritten during any derivation step can be limited by a small constant regardless of other factors.

A Note on the Cooperation in Rewriting Systems with Context-Dependency Checking.

Abstract: This paper discusses the cooperation and its effect on the generative power of rewriting systems with some kind of simple context-dependency checking represented by the mechanism of random context grammars. Specifically, it discusses the cooperation in terms of cooperating distributed grammar systems with respect to all basic types of cooperation protocols, and proves that although the cooperation is powerful enough to increase the generative power of both permitting and forbidding random context grammars, it has no effect on the generative power of random context grammars. It also discusses two possible definitions of the relation of the direct derivation step used in the literature.

Regulated Nondeterminism in PDAs: The Non-Regular Case

Abstract: In this paper, we discuss pushdown automata which can make a nondeterministic decision only if the pushdown content forms a string that belongs to a given control language. It proves that if the control language is linear and non-regular, then the computational power of pushdown automata regulated in this way is increased to the power of Turing machines. Naturally, checking the pushdown content in each computational step is not practically efficient. Therefore, we also prove that two checks of the form of the pushdown content during any computation are sufficient for these automata to be computationally complete. Finally, some descriptional complexity results are discussed.

On pure multi-pushdown automata that perform complete pushdown pops

Abstract: This paper introduces and discusses pure multi-pushdown automata that remove symbols from their pushdowns only by performing complete pushdown pops. This. means that during a pop operation, the entire pushdown is compared with a prefix of the input, and if they match, the whole contents of the pushdown is erased and the input is advanced by the prefix. The paper proves that these automata define an infinite hierarchy of language families identical with the infinite hierarchy of language families resulting from right linear simple matrix grammars. In addition, this paper discusses some other extensions of these automata with respect to operations they can perform with their pushdowns. More specifically, it discusses pure multi-pushdown automata that perform complete pushdown pops that are allowed to join two pushdowns and/or create a new pushdown.

Regulated Nondeterminism in PDAs: The Non-Regular Case

Abstract: In this paper, we discuss pushdown automata which can make a nondeterministic decision only if the pushdown content forms a string that belongs to a given control language It proves that if the control language is linear and non-regular, then the computational power of pushdown automata regulated in this way is increased to the power of Turing machines Naturally, checking the pushdown content in each computational step is not practically efficient Therefore, we also prove that two checks of the form of the pushdown content during any computation are sufficient for these automata to be computationally complete Finally, some descriptional complexity results are discussed

Descriptional Complexity of Three-Nonterminal Scattered Context Grammars: An Improvement

Abstract: z Abstract. Recently, it has been shown that every recursively enumer- able language can be generated by a scattered context grammar with no more than three nonterminals. However, in that construction, the maxi- mal number of nonterminals simultaneously rewritten during a derivation step depends on many factors, such as the cardinality of the alphabet of the generated language and the structure of the generated language itself. This paper improves the result by showing that the maximal number of nonterminals simultaneously rewritten during any derivation step can be limited by a small constant regardless of other factors.