MK-fuzzy Automata and MSO Logics
نویسندگان
چکیده
We introduce MK-fuzzy automata over a bimonoid K which is related to the fuzzification of the McCarthy-Kleene logic. Our automata are inspired by, and intend to contribute to, practical applications being in development in a project on runtime network monitoring based on predicate logic. We investigate closure properties of the class of recognizableMK-fuzzy languages accepted by MKfuzzy automata as well as of deterministically recognizable MK-fuzzy languages accepted by their deterministic counterparts. Moreover, we establish a Nivat-like result for recognizable MK-fuzzy languages. We introduce an MK-fuzzy MSO logic and show the expressive equivalence of a fragment of this logic with MK-fuzzy automata, i.e., a Büchi type theorem.
منابع مشابه
Weighted versus Probabilistic Logics
While a mature theory around logics such as MSO, LTL, and CTL has been developed in the pure boolean setting of finite automata, weighted automata lack such a natural connection with (temporal) logic and related verification algorithms. In this paper, we will identify weighted versions of MSO and CTL that generalize the classical logics and even other quantitative extensions such as probabilist...
متن کاملAutomata and Logics for Unranked and Unordered Trees
In this paper, we consider the monadic second order logic (MSO) and two of its extensions, namely Counting MSO (CMSO) and Presburger MSO (PMSO), interpreted over unranked and unordered trees. We survey classes of tree automata introduced for the logics PMSO and CMSO as well as other related formalisms; we gather results from the literature and sometimes clarify or fill the remaining gaps betwee...
متن کاملWeighted Timed MSO Logics
We aim to generalize Büchi’s fundamental theorem on the coincidence of recognizable and MSO-definable languages to a weighted timed setting. For this, we investigate subclasses of weighted timed automata and show how we can extend existing timed MSO logics with weights. Here, we focus on the class of weighted event-recording automata and define a weighted extension of the full logic MSOer(Σ) in...
متن کاملRelating Paths in Transition Systems: the Fall of the Modal mu-Calculus
This is an extended abstract of a paper presented at MFCS 2015 [11]. Monadic second-order logic (MSO) is considered as a standard for comparing expressiveness of logics of programs. Ground-breaking results concerning expressiveness and decidability of MSO on infinite graphs were obtained first on “freely-generated” structures (words, trees, tree-like structures, etc.) [28,30], then on “non-free...
متن کاملExpressiveness of Monadic Second-Order Logics on Infinite Trees of Arbitrary Branching Degree
In this thesis we study the expressive power of variants of monadic second-order logic (MSO) on infinite trees by means of automata. In particular we are interested in weak MSO and well-founded MSO, where the second-order quantifiers range respectively over finite sets and over subsets of well-founded trees. On finitely branching trees, weak and well-founded MSO have the same expressive power a...
متن کامل