We propose a new algorithm for checking language equivalence of non-deterministic Büchi automata. start from construction proposed by Calbrix, Nivat and Podelski, which makes it possible to reduce the problem that automata on finite words. Although this generates large highly automata, we show how exploit their specific structure apply state-of-the art techniques based coinduction state-space h...

Quantum finite automata with mixed states are proved to be super-exponentially more concise rather than quantum finite automata with pure states. It was proved earlier by A. Ambainis and R. Freivalds that quantum finite automata with pure states can have an exponentially smaller number of states than deterministic finite automata recognizing the same language. There was an unpublished ‘‘folk th...

Neurofuzzy systems—the combination of artificial neural networks with fuzzy logic—have become useful in many application domains. However, conventional neurofuzzy models usually need enhanced representational power for applications that require context and state (e.g., speech, time series prediction, control). Some of these applications can be readily modeled as finite state automata. Previousl...

The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. We also briefly recall the known bounds for the removal of ...

We are interested in the problem of transition reduction of nondeterministic automata. We present some results on the reduction of the automata recognizing the language L(En) denoted by the regular expression En = (1 + ε) · (2 + ε) · (3 + ε) · · · (n+ ε). These results can be used in the general case of the transition reduction problem.

Automata learning is a known technique to infer a finite state machine from a set of observations. In this paper, we revisit Angluin’s original algorithm from a categorical perspective. This abstract view on the main ingredients of the algorithm lays a uniform framework to derive algorithms for other types of automata. We show a straightforward generalization to Moore and Mealy machines, which ...

With the purpose of unifying a number of approaches to energy problems found in the literature, we introduce generalized energy automata. These are finite automata whose edges are labeled with energy functions that define how energy levels evolve during transitions. Uncovering a close connection between energy problems and reachability and Büchi acceptance for semiring-weighted automata, we sho...

It is well known that the language obtained by deleting an arbitrary language from a regular language is regular. We give an upper bound for the state complexity of deleting an arbitrary language from a regular language and a matching lower bound. We show that the state complexity of deletion is n · 2n−1 (respectively, (n + 1 2 ) · 2 − 2) when using complete (respectively, incomplete) determini...

It was proved earlier by A. Ambainis and R. Freivalds that the quantum finite automata with pure states can have exponentially smaller number of states than the deterministic finite automata recognizing the same language. There is a never published “folk theorem” claiming that the quantum finite automata with mixed states are no more than super-exponentially concise than the deterministic finit...

The theory of tree automata was established in the late sixties by Thatcher and Wright [53] and Doner [19]. They showed that the basic logical and algorithmic properties of standard automata theory can be transferred from the domain of finite words to the domain of finite trees (or terms), leading to a theory of regular tree languages. Quoting from the introduction of [53], where the theory of ...