An estimation for the lengths of reduction sequences of the λμρθ\lambda\mu\rho\theta-calculus

Since it was realized that the Curry-Howard isomorphism can be extended to the case of classical logic as well, several calculi have appeared as candidates for the encodings of proofs in classical logic. One of the most extensively studied among them is the $\lambda\mu$-calculus of Parigot. In this paper, based on the result of Xi presented for the $\lambda$-calculus Xi, we give an upper bound for the lengths of the reduction sequences in the $\lambda\mu$-calculus extended with the $\rho$- and $\theta$-rules. Surprisingly, our results show that the new terms and the new rules do not add to the computational complexity of the calculus despite the fact that $\mu$-abstraction is able to consume an unbounded number of arguments by virtue of the $\mu$-rule

On the range of a Jordan *-derivation

summary:In this paper, we examine some questions concerned with certain ``skew'' properties of the range of a Jordan *-derivation. In the first part we deal with the question, for example, when the range of a Jordan *-derivation is a complex subspace. The second part of this note treats a problem in relation to the range of a generalized Jordan *-derivation

Describing Membrane Computations with a Chemical Calculus

Membrane systems are nature motivated computational models inspired by certain basic features of biological cells and their membranes. They are examples of the chemical computational paradigm which describes computation in terms of chemical solutions where molecules interact according to rules de ning their reaction capabilities. Chemical models can be presented by rewriting systems based on multiset manipulations, and they are usually given as a kind of chemical calculus which might also allow nondeterministic and non-sequential computations. Here we study membrane systems from the point of view of the chemical computing paradigm and show how computations of membrane systems can be described by such a chemical calculus

Membrane Systems with Priority, Dissolution, Promoters and Inhibitors and Time Petri Nets

We continue the investigations on exploring the connection between membrane systems and time Petri nets already commenced in [4] by extending membrane systems with promoters/inhibitors, membrane dissolution and priority for rules compared to the simple symbol-object membrane system. By constructing the simulating Petri net, we retain one of the main characteristics of the Petri net model, namely, the firings of the transitions can take place in any order: we do not impose any additional stipulation on the transition sequences in order to obtain a Petri net model equivalent to the general Turing machine. Instead, we substantially exploit the gain in computational strength obtained by the introduction of the timing feature for Petri nets

Simulating Membrane Systems and Dissolution in a Typed Chemical Calculus

We present a transformation of membrane systems, possibly with pro- moter/inhibitor rules, priority relations, and membrane dissolution, into formulas of the chemical calculus such that terminating computations of membranes correspond to terminating reduction sequences of formulas and vice versa. In the end, the same result can be extracted from the underlying computation of the membrane system as from the reduction sequence of the chemical term. The simulation takes place in a typed chemical calculus, but we also give a short account of the untyped case

Membrane Systems and Time Petri Nets

We investigate the relationship of time Petri nets and di erent variants of membrane systems. First we show that the added feature of \time" in time Petri nets makes it possible to simulate the maximal parallel rule application of membrane systems without introducing maximal parallelism to the Petri net semantics, then we de ne local time P systems and explore how time Petri nets and the computations of local time P systems can be related

Absztrakt automaták és formális nyelvek = Abstract Automata and Formal Languages

Monográfiában foglaltuk össze a véges automata hálózatok elméletének alapvető eredményeit . Megadtuk a Leticsevszkij kritérium nélküli automata-hálózatok egy új jellemzését. Megadtunk bizonyos szimbólum osztályokkal ellátott többszalagos automatákat. Megadtuk és vizsgáltuk a kutatásaink során felfedezett automataelméleti elvű új titkosítási rendszert. Új bizonyítást adtunk a Lyndon-Schützenberger tételre és a Shyr-Yu tételre. Általánosítottuk a szavak primitivitásának, illetve periodicitásának fogalmát, s megadtuk, hogy melyek azok a Marcus nyelvtanok, amelyek az adott típusú szavakból álló nyelveket képesek generálni. Sikerült találni egy iterációs lemmát azon környezetfüggetlen nyelvekre, melyek nem lineárisak. A contextuális sztringnyelvek általánosításaként bevezettük és vizsgáltuk a hypergráf contextuális nyelvek és nyelvtanok fogalmát. Automaták segítségével jellemeztük az uniómentes nyelveket. Leírtuk a különféle logikai kalkulusok és valamely levezetési rendszer szabályai szerint megadott levezetések kapcsolatait, s a különféle kalkulusok normalizálhatósági tulajdonságait. Új elvű számítási kutatásainkban az intervallum-értékű számításokat, mint új számítási modellt írtuk le. Digitális geometriai kutatásainkban digitális távolság alapján értelmezett szakaszokat, köröket, hiperbolákat és parabolákat vizsgáltunk. | We summarized in monograph the fundamental results of theory of finite automata networks. We gave a new characterization of automata-networks having no Letichevsky criteria. We gave multi-tape automata supplied by certain symbol classes. We gave and investigated a novel cryptosystem based on automata theory discovered during our research.. We gave a new proof of Lyndon-Schützenberger Theorem and Shyr-Yu Theorem. We generalized the concept of primitivity and periodicity of words and we give the Marcus gramars which are able to generate languages consisting of given type words. It succeed in finding an iteration lemma for non-linear context-free languages. As a generalization of contextual string languages, we introduced and investigated the concept of hypergraph contextual grammars and languages. We characterized the union-free languages by automata. We described the connections of derivations given by various logical calculi and certain derivation system, moreover the normalizable properties of various calculi. In our new computation principle researches we described the intervallum-value computations as new computation model In our digital geometric researches we investigated the sessions, circles, hyperbolas and parabolas defined by a digital distance