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 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 ...

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...

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...

In recent years, two different approaches for learning register automata have been developed: as part of the LearnLib tool algorithms have been implemented that are based on the Nerode congruence for register automata, whereas the Tomte tool implements algorithms that use counterexample-guided abstraction refinement to automatically construct appropriate mappers. In this paper, we compare the L...

Rank-width is a rather new structural graph measure introduced by Oum and Seymour in 2003 in order to find an efficiently computable approximation of clique-width of a graph. Being a very nice graph measure indeed, the only serious drawback of rank-width was that it is virtually impossible to use a given rank-decomposition of a graph for running dynamic algorithms on it. We propose a new indepe...

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...

Efficient learnability using the state merging algorithm is known for a subclass of probabilistic automata termed μ-distinguishable. In this paper, we prove that state merging algorithms can be extended to efficiently learn a larger class of automata. In particular, we show learnability of a subclass which we call μ2-distinguishable. Using an analog of the Myhill-Nerode theorem for probabilisti...

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 ...

Rank-width is a structural graph measure introduced by Oum and Seymour and aimed at better handling of graphs of bounded clique-width. We propose a formal framework and tools for easy design of dynamic algorithms running directly on a rank-decomposition of a graph (on contrary to the usual approach which translates a rankdecomposition into a clique-width expression, with a possible exponential ...