4 research outputs found
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
Algebraic Synchronization Trees and Processes
We study algebraic synchronization trees, i.e., initial solutions of algebraic recursion schemes over the continuous categorical algebra of synchronization trees. In particular, we investigate the relative expressive power of algebraic recursion schemes over two signatures, which are based on those for Basic CCS and Basic Process Algebra, as a means for defining synchronization trees up to isomorphism as well as modulo bisimilarity and language equivalence. The expressiveness of algebraic recursion schemes is also compared to that of the low levels in the Caucal hierarchy