43 research outputs found
Synchronizing weighted automata
We introduce two generalizations of synchronizability to automata with
transitions weighted in an arbitrary semiring K=(K,+,*,0,1). (or equivalently,
to finite sets of matrices in K^nxn.) Let us call a matrix A
location-synchronizing if there exists a column in A consisting of nonzero
entries such that all the other columns of A are filled by zeros. If
additionally all the entries of this designated column are the same, we call A
synchronizing. Note that these notions coincide for stochastic matrices and
also in the Boolean semiring. A set M of matrices in K^nxn is called
(location-)synchronizing if M generates a matrix subsemigroup containing a
(location-)synchronizing matrix. The K-(location-)synchronizability problem is
the following: given a finite set M of nxn matrices with entries in K, is it
(location-)synchronizing?
Both problems are PSPACE-hard for any nontrivial semiring. We give sufficient
conditions for the semiring K when the problems are PSPACE-complete and show
several undecidability results as well, e.g. synchronizability is undecidable
if 1 has infinite order in (K,+,0) or when the free semigroup on two generators
can be embedded into (K,*,1).Comment: In Proceedings AFL 2014, arXiv:1405.527
Automaták , fixpontok, és logika = Automata, fixed points, and logic
Megmutattuk, hogy a vĂ©ges automaták (faautomaták, sĂşlyozott automaták, stb.) viselkedĂ©se vĂ©gesen leĂrhatĂł a fixpont művelet általános tulajdonságainak felhasználásával. Teljes axiomatizálást adtunk a vĂ©ges automaták viselkedĂ©sĂ©t leĂrĂł racionális hatványsorokra Ă©s fasorokra, ill. a vĂ©ges automaták biszimuláciĂł alapĂş viselkedĂ©sĂ©re. Megmutattuk, hogy az automaták elmĂ©letĂ©nek alapvetĹ‘ Kleene tĂ©tele Ă©s általánosĂtásai a fixpont művelet azonosságainak következmĂ©nye. Algebrai eszközökkel vizsgáltuk az elágazĂł idejű temporális logikák Ă©s a monadikus másodrendű logika frágmenseinek kifejezĹ‘ erejĂ©t fákon. FĹ‘ eredmĂ©nyĂĽnk egy olyan kölcsönösen egyĂ©rtelmű kapcsolat kimutatása, amely ezen logikák kifejezĹ‘ erejĂ©nek vizsgálatát visszavezeti vĂ©ges algebrák Ă©s preklĂłnok bizonyos pszeudovarietásainak vizsgálatára. JellemeztĂĽk a reguláris Ă©s környezetfĂĽggetlen nyelvek lexikografikus rendezĂ©seit, vĂ©gtelen szavakra általánosĂtottuk a környezetfĂĽggetlen nyelv fogalmát, Ă©s tisztáztuk ezek számos algoritmikus tulajdonságát. | We have proved that the the bahavior of finite automata (tree automata, weighted automata, etc.) has a finite description with respect to the general properties of fixed point operations. We have obtained complete axiomatizations of rational power series and tree series, and the bisimulation based behavior of finite automata. As an intermediate step of the completeness proofs, we have shown that Kleene's fundamental theorem and its generalizations follow from the equational properties of fixed point operations. We have developed an algebraic framework for describing the expressive power of branching time temporal logics and fragments of monadic second-order logic on trees. Our main results establish a bijective correspondence between these logics and certain pseudo-varieties of finite algebras and/or finitary preclones. We have characterized the lexicographic orderings of the regular and context-free languages and generalized the notion of context-free languages to infinite words and established several of their algorithmic properties
Főnévi csoportok tanulása és felismerése
A dolgozat azt tanulmányozza, hogy fĹ‘nĂ©vi szerkezetek felismerĂ©se milyen rĂ©szproblĂ©mákra bonthatĂł, illetve, hogy az egyes rĂ©szproblĂ©mákban, milyen elemzĂ©sek, teszteredmĂ©nyek segĂtenek bennĂĽnket a továbblĂ©pĂ©sben a lehetĹ‘ legjobb minĹ‘sĂ©gű megoldás felĂ©. A számos megközelĂtĂ©si lehetĹ‘sĂ©g közĂĽl mi a szabály alapĂş mĂłdszereket választottuk, de ez is felvet számos specifikus rĂ©szproblĂ©mát. KĂ©t tanulĂł algoritmust alkalmaztunk szabályok előállĂtására. Az egyik a közismert C4.5, a másik egy saját fejlesztĂ©sű algoritmus, az RGLearn. A teszteket egy erre a cĂ©lra kifejlesztett NP elemzĹ‘vel vĂ©geztĂĽk. A kĂsĂ©rleteket Ă©s a kĂĽlönfĂ©le teszteket jelentĹ‘s mĂ©rtĂ©kben segĂtette a körĂĽlbelĂĽl 1,2 milliĂł szĂłt tartalmazĂł, kĂ©zzel annotált Szeged Korpusz [1], amely kĂĽlönbözĹ‘ (iskolai, szĂ©pirodalomi, számĂtĂłgĂ©pes, jogi, ĂĽzleti) szövegtĂpusokra tartalmazza a nyelvĂ©szeti szakĂ©rtĹ‘k által bejelölt fĹ‘nĂ©vi csoportokat. Az NP felismerĂ©sre kifejlesztett elemzĹ‘nk, szakĂ©rtĹ‘i szabályokkal 65%-os, környezetfĂĽggetlen szabályokkal 85%-os, kömyezetfĂĽggĹ‘ szabályokkal 90%-os pontossággal Ă©pĂtette fel tesztállományban találhatĂł NP szerkezeteket
On the Order Type of Scattered Context-Free Orderings
We show that if a context-free grammar generates a language whose
lexicographic ordering is well-ordered of type less than , then its
order type is effectively computable.Comment: In Proceedings GandALF 2019, arXiv:1909.05979. arXiv admin note: text
overlap with arXiv:1907.1157
Regular expressions for muller context-free languages
Muller context-free languages (MCFLs) are languages of countable words, that is, labeled countable linear orders, generated by Muller context-free grammars. Equivalently, they are the frontier languages of (nondeterministic Muller-)regular languages of infinite trees. In this article we survey the known results regarding MCFLs, and show that a language is an MCFL if and only if it can be generated by a so-called µη-regular expression
Lookahead can help in maximal matching
In this paper we study a problems in the context of fully dynamic graph algorithms that is, when we have to handle updates (insertions and removals of edges), and answer queries regarding the current graph, preferably in a better time bound than running a classical algorithm from scratch each time a query arrives. We show that a maximal matching can be maintained in an (undirected) graph with a deterministic amortized update cost of O(log m) (where m is the all-time maximum number of the edges), provided that a lookahead of length m is available, i.e. we can “peek” the next m update operations in advance