869 research outputs found
AutomatĂĄk, fĂĄk Ă©s logika = Automata, trees and logic
Elemi idejƱ exponenciĂĄlis algoritmus adtunk meg regulĂĄris szavak ekvivalenciĂĄjĂĄnak eldönthetĆsĂ©gĂ©re. ĂltalĂĄnosĂtottuk Kleene tĂ©telĂ©t vĂ©gtelen szavakat is felismerĆ sĂșlyozott automatĂĄkra. KifejlesztettĂŒnk egy algebrai mĂłdszert, amellyel a CTL logika szĂĄmos szegmense estĂ©n eldönthetĆ, hogy egy regulĂĄris fanyelv definiĂĄlhatĂł-e a szegmensben. VizsgĂĄltuk a faautomatĂĄk algebrai tulajdonsĂĄgait, megadtuk a felismerhetĆsĂ©g egy algebrai jellemzĂ©sĂ©t. DefiniĂĄltunk a multi-leszĂĄllĂł fatranszformĂĄtort Ă©s megmutattuk, hogy ekvivalens a determinisztikus regulĂĄris szƱkĂtĂ©sƱ felszĂĄllĂł fatranszformĂĄtorral. MeghatĂĄroztuk a lineĂĄris multi-leszĂĄllĂł osztĂĄly szĂĄmĂtĂĄsi erejĂ©t. Megmutattuk, hogy az alakmegĆrzĆ leszĂĄllĂł fatranszformĂĄtorok ekvivalensek az ĂĄtcĂmkĂ©zĆkkel Ă©s bebizonyĂtottuk, hogy az alakmegĆrzĆ tulajdonsĂĄg eldönthetĆ. Megadtuk a kavics makrĂł fatranszformĂĄciĂłk egy felbontĂĄsĂĄt Ă©s megmutattuk, hogy a kĂŒlönbözĆ cirkularitĂĄsi tulajdonsĂĄgok eldönthetĆk. Ugyancsak megadtuk a felbontĂĄst erĆs kavics kezelĂ©s estĂ©n is. ĂltalĂĄnosĂtottuk J. Engelfriet hiararchia tĂ©telĂ©t sĂșlyozott fatranszformĂĄtorokra. SĂșlyozott faautomatĂĄkra definiĂĄltuk a termĂĄtĂrĂł szemantikĂĄt Ă©s megmutattuk, hogy ekvivalens az algebari szenmatikĂĄval. Algoritmust adtunk annak eldöntĂ©sĂ©re, hogy egy polinomiĂĄlisan sĂșlyozott faautomata vĂ©ges költsĂ©gƱ-e. VizsgĂĄltuk a sĂșlyozott faautomata kĂŒlönbözĆ vĂĄltozatait: fuzzy faautomata, multioperĂĄtor monoid feletti faautomata, Ez utĂłbbi esetre ĂĄltalĂĄnosĂtottuk a Kleene tĂ©telt. | 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
Near-Optimal Scheduling for LTL with Future Discounting
We study the search problem for optimal schedulers for the linear temporal
logic (LTL) with future discounting. The logic, introduced by Almagor, Boker
and Kupferman, is a quantitative variant of LTL in which an event in the far
future has only discounted contribution to a truth value (that is a real number
in the unit interval [0, 1]). The precise problem we study---it naturally
arises e.g. in search for a scheduler that recovers from an internal error
state as soon as possible---is the following: given a Kripke frame, a formula
and a number in [0, 1] called a margin, find a path of the Kripke frame that is
optimal with respect to the formula up to the prescribed margin (a truly
optimal path may not exist). We present an algorithm for the problem; it works
even in the extended setting with propositional quality operators, a setting
where (threshold) model-checking is known to be undecidable
Tree Regular Model Checking for Lattice-Based Automata
Tree Regular Model Checking (TRMC) is the name of a family of techniques for
analyzing infinite-state systems in which states are represented by terms, and
sets of states by Tree Automata (TA). The central problem in TRMC is to decide
whether a set of bad states is reachable. The problem of computing a TA
representing (an over- approximation of) the set of reachable states is
undecidable, but efficient solutions based on completion or iteration of tree
transducers exist. Unfortunately, the TRMC framework is unable to efficiently
capture both the complex structure of a system and of some of its features. As
an example, for JAVA programs, the structure of a term is mainly exploited to
capture the structure of a state of the system. On the counter part, integers
of the java programs have to be encoded with Peano numbers, which means that
any algebraic operation is potentially represented by thousands of applications
of rewriting rules. In this paper, we propose Lattice Tree Automata (LTAs), an
extended version of tree automata whose leaves are equipped with lattices. LTAs
allow us to represent possibly infinite sets of interpreted terms. Such terms
are capable to represent complex domains and related operations in an efficient
manner. We also extend classical Boolean operations to LTAs. Finally, as a
major contribution, we introduce a new completion-based algorithm for computing
the possibly infinite set of reachable interpreted terms in a finite amount of
time.Comment: Technical repor
Lukasiewicz mu-Calculus
We consider state-based systems modelled as coalgebras whose type incorporates branching, and show that by suitably adapting the definition of coalgebraic bisimulation, one obtains a general and uniform account of the linear-time behaviour of a state in such a coalgebra. By moving away from a boolean universe of truth values, our approach can measure the extent to which a state in a system with branching is able to exhibit a particular linear-time behaviour. This instantiates to measuring the probability of a specific behaviour occurring in a probabilistic system, or measuring the minimal cost of exhibiting a specific behaviour in the case of weighted computations
Intangibles mismeasurements, synergy, and accounting numbers : a note.
For the last two decades, authors (e.g. Ohlson, 1995; Lev, 2000, 2001) have regularly pointed out the enforcement of limitations by traditional accounting frameworks on financial reporting informativeness. Consistent with this claim, it has been then argued that accounting finds one of its major limits in not allowing for direct recognition of synergy occurring amongst the firm intangible and tangible items (Casta, 1994; Casta & Lesage, 2001). Although the firm synergy phenomenon has been widely documented in the recent accounting literature (see for instance, Hand & Lev, 2004; Lev, 2001) research hitherto has failed to provide a clear approach to assess directly and account for such a henceforth fundamental corporate factor. The objective of this paper is to raise and examine, but not address exhaustively, the specific issues induced by modelling the synergy occurring amongst the firm assets whilst pointing out the limits of traditional accounting valuation tools. Since financial accounting valuation methods are mostly based on the mathematical property of additivity, and consequently may occult the perspective of regarding the firm as an organized set of assets, we propose an alternative valuation approach based on non-additive measures issued from the Choquet's (1953) and Sugeno's (1997) framework. More precisely, we show how this integration technique with respect to a non-additive measure can be used to cope with either positive or negative synergy in a firm value-building process and then discuss its potential future implications for financial reporting.Financial reporting; accounting goodwill; assets synergy; non-additive measures; Choquetâs framework;
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