We consider weighted finite automata over strong bimonoids, where these weight structures can be considered as semirings which might lack distributivity. Then, in general, the well-known run semantics, initial algebra semantics, and transition semantics of an automaton are different. We prove an algebraic characterization for the initial algebra semantics in terms of stable finitely generated s...

We present an active learning algorithm named NRTALearning for nondeterministic real-time automata (NRTAs). Real-time (RTAs) are a subclass of timed with only one clock which resets at each transition. First, we prove the corresponding Myhill-Nerode theorem languages. Then show that there exists unique minimal deterministic automaton (DRTA) recognizing given language, but same does not hold NRT...

It is well known that finite square matrices over a Kleene algebra again form a Kleene algebra. This is also true for infinite matrices under suitable restrictions. One can use this fact to solve certain infinite systems of inequalities over a Kleene algebra. Automatic systems are a special class of infinite systems that can be viewed as infinite-state automata. Automatic systems can be collaps...

There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOL-based theorem provers. The reason is that they need to be represented as graphs, matrices or functions, none of which are inductive datatypes. Als...

Guarded strings are like ordinary strings over a finite alphabet P, except that atoms of the free Boolean algebra on a set of atomic tests B alternate with the symbols of P. The regular sets of guarded strings play the same role in Kleene algebra with tests as the regular sets of ordinary strings do in Kleene algebra. In this paper we develop the elementary theory of finite automata on guarded ...

Abstract We present an algorithm to learn a deterministic timed automaton (DTA) via membership and equivalence queries. Our is extension of the L* with Myhill-Nerode style characterization recognizable languages, which class languages by DTAs. first characterize Nerode-style congruence. Using it, we give smart teacher answering symbolic queries in addition With query, one can ask certain set wo...

This paper presents a polynomial-time algorithm for the inclusion problem for a large class of regular expressions. The algorithm is not based on construction of finite automata, and can therefore be faster than the lower bound implied by the Myhill-Nerode theorem. The algorithm automatically discards irrelevant parts of the right-hand expression. The irrelevant parts of the right-hand expressi...

We present a novel canonical automaton model for languages over infinite data domains, that is suitable for specifying the behavior of services, protocol components, interfaces, etc. The model is based on register automata. A major contribution is a construction of succinct canonical register automata, which is parameterized on the set of relations by which elements in the data domain can be co...

We study the problem of how to learn tree transformations on a given regular tree domain from a finite sample of input-output examples. We assume that the target tree transformation can be defined by a deterministic top-down tree transducer with regular domain inspection (DTopIreg). An rpni style learning algorithm that solves this problem in polynomial time and with polynomially many examples ...

The distinguishability language of a regular language L is the set of words distinguishing between pairs of words under the Myhill-Nerode equivalence induced by L, i.e., between pairs of distinct left quotients of L. The similarity relation induced by a language L is a similarity relation inspired by the Myhill-Nerode equivalence and it was used to obtain compact representation of automata for ...