A characterization of Büchi tree automata

We show that a language of infinite binary trees is definable by a Σ₂-formula of the monadic second order logic of two successors (with no additional symbols) iff it can be accepted by a Büchi automaton. The same result has been obtained by G. Lenzi, but our proof is simpler.     

Observations on determinization of Büchi automata

The two determinization procedures of Safra and Muller–Schupp for Büchi automata are compared, based on an implementation in a program called OmegaDet.     

A power-set construction for reducing Büchi automata to non-determinism degree two

Büchi automata are finite automata that accept languages of infinitely long strings, so-called ω-languages. It is well known that, unlike in the finite-string case, deterministic and non-deterministic Büchi automata accept different ω-language classes, i.e., that determination of a non-deterministic Büchi automaton using the classical power-set construction will yield in general a deterministic Büchi automaton which accepts a superset of the ω-language accepted by the given non-deterministic automaton.In this paper, a power-set construction to a given Büchi automaton is presented, which reduces the degree of non-determinism of the automaton to at most two, meaning that to each state and input symbol, there exist at most two distinct successor states. The constructed Büchi automaton of non-determinism degree two and the given Büchi automaton of arbitrary non-determinism degree will accept the same ω-language.     

A framework to visualize equivalences between computational models of regular languages

We discuss how to increase and simplify the understanding of the equivalence relations between machine models and/or language representations of formal languages by means of the animation tool SAGEMoLiC. Our new educational tool permits the simulation of the execution of models of computation, as many other animation systems do, but its philosophy goes further than these of the usual systems since it allows for a true visualization of the key notions involved in the formal proofs of these equivalences. In contrast with the proposal of previous systems, our approach to visualize equivalence theorems is not a simple “step by step animation” of specific conversion algorithms between computational models and/or grammatical representations of formal languages, because we make emphasis on the key theoretical notions involved in the formal proofs of these equivalences.     

A characterization of (regular) circular languages generated by monotone complete splicing systems

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for monotone complete systems, which are finite circular splicing systems with rules of a simpler form. We show that a circular language L is generated by a monotone complete system if and only if the set Lin(L) of all words corresponding to L is a pure unitary language generated by a set closed under the conjugacy relation. The class of pure unitary languages was introduced by A. Ehrenfeucht, D. Haussler, G. Rozenberg in 1983, as a subclass of the class of context-free languages, together with a characterization of regular pure unitary languages by means of a decidable property. As a direct consequence, we characterize (regular) circular languages generated by monotone complete systems. We can also decide whether the language generated by a monotone complete system is regular. Finally, we point out that monotone complete systems have the same computational power as finite simple systems, an easy type of circular splicing system defined in the literature from the very beginning, when only one rule of a specific type is allowed. From our results on monotone complete systems, it follows that finite simple systems generate a class of languages containing non-regular languages, showing the incorrectness of a longstanding result on simple systems.     

The equivalence problem for deterministic MSO tree transducers is decidable

It is decidable for deterministic MSO definable graph-to-string or graph-to-tree transducers whether they are equivalent on a context-free set of graphs.     

Folk theorems on the determinization and minimization of timed automata

Timed automata are known not to be complementable or determinizable. Natural questions are, then, could we check whether a given TA enjoys these properties? These problems are not algorithmically solvable. Minimizing the “resources” of a TA (number of clocks or size of constants) are also unsolvable problems. In this paper we provide simple undecidability proofs using a “constructive” version of the problems where we require not just a yes/no answer, but also a “witness”. Proofs are then simple reductions from the universality problem. Recent work of Finkel shows that the corresponding decision problems are also undecidable [O. Finkel, On decision problems for timed automata, Bulletin of the European Association for Theoretical Computer Science 87 (2005) 185-190].     

Feedback automata and their languages

We introduce families of languages which are generated by deterministic and nondeterministic feedback-controlled models of automata. In case of the two deterministic models considered, the generated families are proper subclasses of the family of regular languages, where, in case of the nondeterministic model, the generated family equals the family of ?-free regular languages.     

Boolean operations and inclusion test for attribute–element constraints

The history of schema languages for XML is (roughly) an increase of expressiveness. While early schema languages mainly focused on the element structure, Clark first paid an equal attention to attributes by allowing both element and attribute constraints in a single constraint expression (we call his mechanism “attribute–element constraints”). In this paper, we investigate intersection and difference operations and inclusion test for attribute–element constraints, in view of their importance in static typechecking for XML processing programs. The contributions here are (1) proofs of closure under intersection and difference as well as decidability of inclusion test and (2) algorithm formulations incorporating a “divide-and-conquer” strategy for avoiding an exponential blow-up for typical inputs.     

Compositional synthesis of asynchronous automata

Asynchronous automata are a model of communication processes with a control structure distributed on a set P of processes, global initializations and global accepting conditions. The well-known theorem of Zielonka states that they recognize exactly the class of regular Mazurkiewicz trace languages. The corresponding synthesis problem is, given a global specification A of any regular trace language L, to build an asynchronous automaton that recognizes L, automatically. Yet, all such existing constructions are quite involved and yield an explosion of the number of states in each process, which is exponential in both the sizes of A and P. In this paper, we introduce the particular case of distributed asynchronous automata, which require that the initializations and the accepting conditions are distributed as well. We present an original technique based on simple compositions/decompositions of these distributed asynchronous automata that results in the construction of smaller non-deterministic asynchronous automata: now, the number of states in each process is only polynomial in the size of A, but is still exponential in the size of P.     

Minimal forbidden subwords

Motivated by a study of similar problems stated for factors of words, we study forbidden subwords of a language or a word. A procedure for obtaining the set of all words avoiding a given set of subwords is presented. On the other hand, an algorithm for computing the set of minimal forbidden subwords for a word is given. The case of a two-letter alphabet appears to be particularly interesting and it is considered separately.     

Storage Products and Linear Control of Derivations

Various automata using certain kinds of tuples of storages are defined in the literature. In this paper we investigate some possibilities to define such storages independently of automata by a restricted type of product on storages, called concatenation. It is shown that there is a strong relation between automata with concatenated pushdowns and restricted classes of linear controlled grammars. Using this result, some relations between hierarchies of automata with an ascending number of concatenated pushdowns and some well-known hierarchies of controlled grammars follow naturally.     

A note on equations for commutative regular languages

In this note we prove that the equations satisfied by one-letter regular languages are exactly those satisfied by commutative regular languages. This answers a problem raised by Arto Salomaa.     

A general comparison of language learning from examples and from queries

In language learning, strong relationships between Gold-style models and query models have recently been observed: in some quite general setting Gold-style learners can be replaced by query learners and vice versa, without loss of learning capabilities. These ‘equalities’ hold in the context of learning indexable classes of recursive languages.