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Workshop "Formale Methoden der Linguistik" und "14. Theorietag Automaten und Formale Sprachen"
(2004)
We introduce and investigate input-revolving finite automata, which are (nondeterministic) finite state automata with the additional ability to shift the remaining part of the input. Three different modes of shifting are considered, namely revolving to the left, revolving to the right, and circular-interchanging. We investigate the computational capacities of these three types of automata and their deterministic variants, comparing any of the six classes of automata with each other and with further classes of well-known automata. In particular, it is shown that nondeterminism is better than determinism, that is, for all three modes of shifting there is a language accepted by the nondeterministic model but not accepted by any deterministic automaton of the same type. Concerning the closure properties most of the deterministic language families studied are not closed under standard operations. For example, we show that the family of languages accepted by deterministic right-revolving finite automata is an anti-AFL which is not closed under reversal and intersection.
It is proved that the number of components in context-free cooperating distributed (CD) grammar systems can be reduced to 3 when they are working in the so-called sf-mode of derivation, which is the cooperation protocol which has been considered first for CD grammar systems. In this derivation mode, a component continues the derivation until and unless there is a nonterminal in the sentential form which cannot be rewritten according to that component. Moreover, it is shown that CD grammar systems in sf-mode with only one component can generate only the context-free languages but they can generate non-context-free languages if two components are used. The sf-mode of derivation is compared with other well-known cooperation protocols with respect to the hierarchies induced by the number of components. (C) 2004 Elsevier B.V. All rights reserved
The power of a language L is the set of all powers of the words in L. In this paper, the following decision problem is investigated. Given a context-free language L, is the power of L context-free? We show that this problem is decidable for languages over unary alphabets, but it is undecidable whenever languages over alphabets with at least two letters are considered. (C) 2003 Elsevier B.V. All rights reserved
Parsability approaches of several grammar formalisms generating also non-context-free languages are explored. Chomsky grammars, Lindenmayer systems, grammars with controlled derivations, and grammar systems are treated. Formal properties of these mechanisms are investigated, when they are used as language acceptors. Furthermore, cooperating distributed grammar systems are restricted so that efficient deterministic parsing without backtracking becomes possible. For this class of grammar systems, the parsing algorithm is presented and the feature of leftmost derivations is investigated in detail.
Grammars with valuations are context-free rewriting mechanisms where the derivation process is controlled by a recursive function that evaluates strings. They have been introduced by Jurgen Dassow as models for the molecular replication process taking into account its selective character. A symbol is active in a grammar with valuation if it can be rewritten non-identically. This paper studies the effect of restricting the number of active symbols in grammars with valuations and several variants thereof to their generative power. It is investigated in which cases the number of active symbols induces infinite strict hierarchies and when the hierarchies collapse. The induced language families are compared among one another. (C) 2016 Elsevier B.V. All rights reserved.
We propose a solution based on networks of picture processors to the problem of picture pattern matching. The network solving the problem can be informally described as follows: it consists of two subnetworks, one of them extracts at each step, simultaneously, all subpictures of identical (progressively decreasing) size from the input picture and sends them to the other subnetwork which checks whether any of the received pictures is identical to the pattern. We present an efficient solution based on networks with evolutionary processors only, for patterns with at most three rows or columns. Afterward, we present a solution based on networks containing both evolutionary and hiding processors running in O(n + m + kl) computational (processing and communication) steps, for any size (n, m) of the input pic-ture and (k, l) of the pattern. From the proofs of these results, we infer that any (k, l)-local language with 1 <= k <= 3 can be decided in O(n + m + l) computational steps by networks with evolutionary processors only, while any (k, l)-local language with arbitrary k, l can be decided in O(n + m + kl) computational steps by networks containing both evolutionary and hiding processors.
We define H- and EH-expressions as extensions of regular expressions by adding homomorphic and iterated homomorphic replacement as new operations, resp. The definition is analogous to the extension given by Gruska in order to characterize context-free languages. We compare the families of languages obtained by these extensions with the families of regular, linear context-free, context-free, and EDT0L languages. Moreover, relations to language families based on patterns, multi-patterns, pattern expressions, H-systems and uniform substitutions are also investigated. Furthermore, we present their closure properties with respect to TRIO operations and discuss the decidability status and complexity of fixed and general membership, emptiness, and the equivalence problem.
Iterated finite state sequential transducers are considered as language generating devices. The hierarchy induced by the size of the state alphabet is proved to collapse to the fourth level. The corresponding language families are related to the families of languages generated by Lindenmayer systems and Chomsky grammars. Finally, some results on deterministic and extended iterated finite state transducers are established.
We consider generating and accepting programmed grammars with bounded degree of non-regulation, that is, the maximum number of elements in success or in failure fields of the underlying grammar. In particular, it is shown that this measure can be restricted to two without loss of descriptional capacity, regardless of whether arbitrary derivations or left-most derivations are considered. Moreover, in some cases, precise characterizations of the linear bounded automaton problem in terms of programmed grammars are obtained. Thus, the results presented in this paper shed new light on some longstanding open problem in the theory of computational complexity.