Remarks on the Computational Power of Some Restricted Variants of P Systems with Active Membranes

In this paper we consider three restricted variants of P systems with active membranes: (1) P systems using out communication rules only, (2) P systems using elementary membrane division and dissolution rules only, and (3) polarizationless P systems using dissolution and restricted evolution rules only. We show that every problem in P can be solved with uniform families of any of these variants. This, using known results on the upper bound of the computational power of variants (1) and (3) yields new characterizations of the class P. In the case of variant (2) we provide a further characterization of P by giving a semantic restriction on the computations of P systems of this varian

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A Characterization of PSPACE with Antimatter and Membrane Creation

The use of negative information provides a new tool for exploring the limits of P systems as computational devices. In this paper we prove that the combination of antimatter and annihilation rules (based on the annihilation of physical particles and antiparticles) and membrane creation (based on autopoiesis) provides a P system model able to solve PSPACE-complete problems. Namely, we provide a uniform family of P system in such P system model which solves the satis ability problem for quanti ed Boolean formulas (QSAT). In the second part of the paper, we prove that all the decision problems which can be solved with this P system model belong to the complexity class PSPACE, so this P system model characterises PSPACE.Ministerio de Economía y Competitividad TIN2012-3743

Hierarchies of tree series transformations

AbstractWe study bottom-up and top-down tree series transducers over a semiring A and denote the tree series transformation classes computed by them by BOTt−ts(A) and TOPt−ts(A), respectively. We present the inclusion diagram of the classes p-BOTt−tsn(A), p-TOPt−tsn(A), p-BOTt−tsn+1(A), and p-TOPt−tsn+1(A) and prove its correctness, where A is a commutative izz-semiring (izz=idempotent, zero-divisor free, and zero-sum free) and the prefix p stands for polynomial. This inclusion diagram implies the properness of the following four hierarchies: p-TOPt−ts(A)⊆p-TOPt−ts2(A)⊆p-TOPt−ts3(A)⊆⋯,p-BOTt−ts(A)⊆p-BOTt−ts2(A)⊆p-BOTt−ts3(A)⊆⋯,p-TOPt−ts(A)⊆p-BOTt−ts2(A)⊆p-TOPt−ts3(A)⊆p-BOTt−ts4(A)⊆⋯,p-BOTt−ts(A)⊆p-TOPt−ts2(A)⊆p-BOTt−ts3(A)⊆p-TOPt−ts4(A)⊆⋯,where the first hierarchy generalizes the famous top-down tree transformation hierarchy of Engelfriet (Math. Systems Theory 15 (1982) 95–125). As the second main result we prove that the first two hierarchies are proper even for arbitrary (i.e., not necessarily commutative) izz-semirings

Weighted languages recognizable by weighted tree automata

Yields of recognizable weighted tree languages, yields of local weighted tree languages, and weighted context-free languages are related. It is shown that the following five classes of weighted languages are the same: (i) the class of weighted languages generated by plain weighted context-free grammars, (ii) the class of weighted languages recognized by plain weighted tree automata, (iii) the class of weighted languages recognized by deterministic and plain topdown weighted tree automata, (iv) the class of weighted languages recognized by deterministic and plain bottom-up weighted tree automata, and (v) the class of weighted languages determined by plain weighted local systems

Automaták, fák és logika = Automata, trees and logic

Elemi idejű exponenciális algoritmus adtunk meg reguláris szavak ekvivalenciájának eldönthetőségére. Általánosítottuk Kleene tételét végtelen szavakat is felismerő súlyozott automatákra. Kifejlesztettünk egy algebrai módszert, amellyel a CTL logika számos szegmense estén eldönthető, hogy egy reguláris fanyelv definiálható-e a szegmensben. Vizsgáltuk a faautomaták algebrai tulajdonságait, megadtuk a felismerhetőség egy algebrai jellemzését. Definiáltunk a multi-leszálló fatranszformátort és megmutattuk, hogy ekvivalens a determinisztikus reguláris szűkítésű felszálló fatranszformátorral. Meghatároztuk a lineáris multi-leszálló osztály számítási erejét. Megmutattuk, hogy az alakmegőrző leszálló fatranszformátorok ekvivalensek az átcímkézőkkel és bebizonyítottuk, hogy az alakmegőrző tulajdonság eldönthető. Megadtuk a kavics makró fatranszformációk egy felbontását és megmutattuk, hogy a különböző cirkularitási tulajdonságok eldönthetők. Ugyancsak megadtuk a felbontást erős kavics kezelés estén is. Általánosítottuk J. Engelfriet hiararchia tételét súlyozott fatranszformátorokra. Súlyozott faautomatákra definiáltuk a termátíró szemantikát és megmutattuk, hogy ekvivalens az algebari szenmatikával. Algoritmust adtunk annak eldöntésére, hogy egy polinomiálisan súlyozott faautomata véges költségű-e. Vizsgáltuk a súlyozott faautomata különböző változatait: fuzzy faautomata, multioperátor monoid feletti faautomata, Ez utóbbi esetre általánosítottuk a Kleene tételt. | We gave an elementary algorithm for deciding the equivalence of regular words. We generalized Kleene's theorem to weighted automata processing infinite words. We developed an algebraic method that, for several segments of the CTL logic, can be applied to decide if a regular tree language can be defined in that segment. We examined algebraic properties of tree automata, and gave an algebraic characterization of recognizability. We defined multi bottom-up tree transducers and showed that they are equivalent to top-down tree transducers with regular look-ahead. We determined the computation power of the linear subclass. We showed that shape preserving bottom-up tree transducers are equivalent to relabelings. We proved that the shape preserving property is decidable. We gave a decomposition for pebble macro tree transducers and showed that certain circularity properties are decidable. We also gave a decomposition for the strong pebble handling. We have generalized the hierarchy theorem of J. Engelfriet to weighted tree transducers. We defined the term rewrite semantics of weighted tree transducers and showed that it is equivalent to the algebraic semantics. We gave a decision algorithm for the finite cost property of a polynomially weighted tree automata. We defined different versions of weighted tree automata: fuzzy tree automata, weighted tree automata over a multioperator monoid. For the latter we generalized Kleene's theorem