Martin Kutrib

Bio: Martin Kutrib is an academic researcher from University of Giessen. The author has contributed to research in topics: Nested word & Nondeterministic finite automaton. The author has an hindex of 23, co-authored 292 publications receiving 2726 citations.

Nondeterministic descriptional complexity of regular languages

Abstract: We investigate the descriptional complexity of operations on finite and infinite regular languages over unary and arbitrary alphabets. The languages are represented by nondeterministic finite automata (NFA). In particular, we consider Boolean operations, catenation operations – concatenation, iteration, λ-free iteration – and the reversal. Most of the shown bounds are tight in the exact number of states, i.e. the number is sufficient and necessary in the worst case. Otherwise tight bounds in the order of magnitude are shown.

Descriptional and computational complexity of finite automata---A survey

Abstract: Finite automata are probably best known for being equivalent to right-linear context-free grammars and, thus, for capturing the lowest level of the Chomsky-hierarchy, the family of regular languages. Over the last half century, a vast literature documenting the importance of deterministic, nondeterministic, and alternating finite automata as an enormously valuable concept has been developed. In the present paper, we tour a fragment of this literature. Mostly, we discuss developments relevant to finite automata related problems like, for example, (i) simulation of and by several types of finite automata, (ii) standard automata problems such as fixed and general membership, emptiness, universality, equivalence, and related problems, and (iii) minimization and approximation. We thus come across descriptional and computational complexity issues of finite automata. We do not prove these results but we merely draw attention to the big picture and some of the main ideas involved.

State complexity of basic operations on nondeterministic finite automata

Abstract: The state complexities of basic operations on nondeterministic finite automata (NFA) are investigated. In particular, we consider Boolean operations, catenation operations - concatenation, iteration, λ-free iteration - and the reversal on NFAs that accept finite and infinite languages over arbitrary alphabets. Most of the shown bounds are tight in the exact number of states, i.e. the number is sufficient and necessary in the worst case. For the complementation tight bounds in the order of magnitude are proved. It turns out that the state complexities of operations on NFAs and deterministic finite automata (DFA) are quite different. For example, the reversal and concatenation have exponential state complexity on DFAs but linear complexity on NFAs. Conversely, the complementation can be done with linear complexity on DFAs but needs exponentially many states on NFAs.

Mathematical Theory of Computation

Abstract: : This project was concerned with the development of correct and reusable software through the use of higher order abstractions (function, control, assignment, process) and reflection. A semantic framework for these notions will be the basis of an experimental system for manipulating and reasoning about programs. The goals of this project were the development of logical formalisms for reasoning about programs that use abstractions and reflection, and the application of these theoretical results to selected software problems. Example applications include (1) clarification of existing programming paradigms, (2) analysis of existing and proposed languages used in the DARPA community for specifying, writing, and transforming programs, and (3) development and implementation of tools for computer aided reasoning about and operating on programs. The accomplishments of this project fit into four categories: (1) logics for reasoning about function and control abstractions; (2) logics for reasoning about data mutation; (3) logics for reasoning about function and control abstractions in the presence of mutable data; and (4) applying methodology for reasoning about programs to the mechanical verification of hardware.

Descriptional and computational complexity of finite automata---A survey

Abstract: Finite automata are probably best known for being equivalent to right-linear context-free grammars and, thus, for capturing the lowest level of the Chomsky-hierarchy, the family of regular languages. Over the last half century, a vast literature documenting the importance of deterministic, nondeterministic, and alternating finite automata as an enormously valuable concept has been developed. In the present paper, we tour a fragment of this literature. Mostly, we discuss developments relevant to finite automata related problems like, for example, (i) simulation of and by several types of finite automata, (ii) standard automata problems such as fixed and general membership, emptiness, universality, equivalence, and related problems, and (iii) minimization and approximation. We thus come across descriptional and computational complexity issues of finite automata. We do not prove these results but we merely draw attention to the big picture and some of the main ideas involved.

Descriptional Complexity of Machines with Limited Resources.

Abstract: Over the last 30 years or so many results have appeared on the descriptional complexity of machines with limited resources. Since these results have appeared in a variety of different contexts, our goal here is to provide a survey of these results. Partic- ular emphasis is put on limiting resources (e.g., nondeterminism, ambiguity, lookahead, etc.) for various types of finite state machines, pushdown automata, parsers and cellu- lar automata and on the effect it has on their descriptional complexity. We also address the question of how descriptional complexity might help in the future to solve practical issues, such as software reliability.

State complexity of some operations on binary regular languages

Abstract: We investigate the state complexity of some operations on binary regular languages. In particular, we consider the concatenation of languages represented by deterministic finite automata, and the reversal and complementation of languages represented by nondeterministic finite automata. We prove that the upper bounds on the state complexity of these operations, which were known to be tight for larger alphabets, are tight also for binary alphabets.