A Formal Approach based on Fuzzy Logic for the Specification of Component-Based Interactive Systems

Formal methods are widely recognized as a powerful engineering method for the specification, simulation, development, and verification of distributed interactive systems. However, most formal methods rely on a two-valued logic, and are therefore limited to the axioms of that logic: a specification is valid or invalid, component behavior is realizable or not, safety properties hold or are violated, systems are available or unavailable. Especially when the problem domain entails uncertainty, impreciseness, and vagueness, the appliance of such methods becomes a challenging task. In order to overcome the limitations resulting from the strict modus operandi of formal methods, the main objective of this work is to relax the boolean notion of formal specifications by using fuzzy logic. The present approach is based on Focus theory, a model-based and strictly formal method for componentbased interactive systems. The contribution of this work is twofold: i) we introduce a specification technique based on fuzzy logic which can be used on top of Focus to develop formal specifications in a qualitative fashion; ii) we partially extend Focus theory to a fuzzy one which allows the specification of fuzzy components and fuzzy interactions. While the former provides a methodology for approximating I/O behaviors under imprecision, the latter enables to capture a more quantitative view of specification properties such as realizability.Comment: In Proceedings FESCA 2015, arXiv:1503.0437

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

Separable GPL: Decidable Model Checking with More Non-Determinism

Generalized Probabilistic Logic (GPL) is a temporal logic, based on the modal mu-calculus, for specifying properties of branching probabilistic systems. We consider GPL over branching systems that also exhibit internal non-determinism under linear-time semantics (which is resolved by schedulers), and focus on the problem of finding the capacity (supremum probability over all schedulers) of a fuzzy formula. Model checking GPL is undecidable, in general, over such systems, and existing GPL model checking algorithms are limited to systems without internal non-determinism, or to checking non-recursive formulae. We define a subclass, called separable GPL, which includes recursive formulae and for which model checking is decidable. A large class of interesting and decidable problems, such as termination of 1-exit Recursive MDPs, reachability of Branching MDPs, and LTL model checking of MDPs, whose decidability has been studied independently, can be reduced to model checking separable GPL. Thus, GPL is widely applicable and, with a suitable extension of its semantics, yields a uniform framework for studying problems involving systems with non-deterministic and probabilistic behaviors