6 research outputs found
Synchronous Subsequentiality and Approximations to Undecidable Problems
We introduce the class of synchronous subsequential relations, a subclass of
the synchronous relations which embodies some properties of subsequential
relations. If we take relations of this class as forming the possible
transitions of an infinite automaton, then most decision problems (apart from
membership) still remain undecidable (as they are for synchronous and
subsequential rational relations), but on the positive side, they can be
approximated in a meaningful way we make precise in this paper. This might make
the class useful for some applications, and might serve to establish an
intermediate position in the trade-off between issues of expressivity and
(un)decidability.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Linearly bounded infinite graphs
Linearly bounded Turing machines have been mainly studied as acceptors for
context-sensitive languages. We define a natural class of infinite automata
representing their observable computational behavior, called linearly bounded
graphs. These automata naturally accept the same languages as the linearly
bounded machines defining them. We present some of their structural properties
as well as alternative characterizations in terms of rewriting systems and
context-sensitive transductions. Finally, we compare these graphs to rational
graphs, which are another class of automata accepting the context-sensitive
languages, and prove that in the bounded-degree case, rational graphs are a
strict sub-class of linearly bounded graphs
Boolean Algebras from Trace Automata
We consider trace automata. Their vertices are Mazurkiewicz traces and they accept finite words. Considering the length of a trace as the length of its Foata normal form, we define the operations of level-length synchronization and of superposition of trace automata. We show that if a family F of trace automata is closed under these operations, then for any deterministic automaton H in F, the word languages accepted by the deterministic automata of F that are length-reducible to H form a Boolean algebra. We show that the family of trace suffix automata with level-regular contexts and the subfamily of vector addition systems satisfy these closure properties. In particular, this yields various Boolean algebras of word languages accepted by deterministic vector addition systems
Families of automata characterizing context-sensitive languages
International audienceIn the hierarchy of infinite graph families, rational graphs are defined by rational transducers with labelled final states. This paper proves that their traces are precisely context-sensitive languages and that this result remains true for synchronized rational graphs
Solving Infinite Games in the Baire Space
Infinite games (in the form of Gale-Stewart games) are studied where a play
is a sequence of natural numbers chosen by two players in alternation, the
winning condition being a subset of the Baire space . We
consider such games defined by a natural kind of parity automata over the
alphabet , called -MSO-automata, where transitions are
specified by monadic second-order formulas over the successor structure of the
natural numbers. We show that the classical B\"uchi-Landweber Theorem (for
finite-state games in the Cantor space ) holds again for the present
games: A game defined by a deterministic parity -MSO-automaton is
determined, the winner can be computed, and an -MSO-transducer
realizing a winning strategy for the winner can be constructed.Comment: Minor revision. 26 pages, 1 figur
Query containment and rewriting using views for regular path queries under constraints
ABSTRACT In this paper we consider general path constraints for semistructured databases. Our general constraints do not suffer from the limitations of the path constraints previously studied in the literature. We investigate the containment of regular path queries under general path constraints. We show that when the path constraints and queries are expressed by words, as opposed to languages, the containment problem becomes equivalent to the word rewrite problem for a corresponding semi-Thue system. Consequently, if the corresponding semi-Thue system has an undecidable word problem, the word query containment problem will be undecidable too. Also, we show that there are word constraints, where the corresponding semi-Thue system has a decidable word rewrite problem, but the general query containment under these word constraints is undecidable. In order to overcome this, we exhibit a large, practical class of word constraints with a decidable general query containment problem. Based on the query containment under constraints, we reason about constrained rewritings -using views-of regular path queries. We give a constructive characterization for computing optimal constrained rewritings using views