1,158 research outputs found
Unified Analysis of Collapsible and Ordered Pushdown Automata via Term Rewriting
We model collapsible and ordered pushdown systems with term rewriting, by
encoding higher-order stacks and multiple stacks into trees. We show a uniform
inverse preservation of recognizability result for the resulting class of term
rewriting systems, which is obtained by extending the classic saturation-based
approach. This result subsumes and unifies similar analyses on collapsible and
ordered pushdown systems. Despite the rich literature on inverse preservation
of recognizability for term rewrite systems, our result does not seem to follow
from any previous study.Comment: in Proc. of FRE
Reachability analysis of first-order definable pushdown systems
We study pushdown systems where control states, stack alphabet, and
transition relation, instead of being finite, are first-order definable in a
fixed countably-infinite structure. We show that the reachability analysis can
be addressed with the well-known saturation technique for the wide class of
oligomorphic structures. Moreover, for the more restrictive homogeneous
structures, we are able to give concrete complexity upper bounds. We show ample
applicability of our technique by presenting several concrete examples of
homogeneous structures, subsuming, with optimal complexity, known results from
the literature. We show that infinitely many such examples of homogeneous
structures can be obtained with the classical wreath product construction.Comment: to appear in CSL'1
Timed pushdown automata revisited
This paper contains two results on timed extensions of pushdown automata
(PDA). As our first result we prove that the model of dense-timed PDA of
Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with
timeless stack. Motivated by this result, we advocate the framework of
first-order definable PDA, a specialization of PDA in sets with atoms, as the
right setting to define and investigate timed extensions of PDA. The general
model obtained in this way is Turing complete. As our second result we prove
NEXPTIME upper complexity bound for the non-emptiness problem for an expressive
subclass. As a byproduct, we obtain a tight EXPTIME complexity bound for a more
restrictive subclass of PDA with timeless stack, thus subsuming the complexity
bound known for dense-timed PDA.Comment: full technical report of LICS'15 pape
Multipebble Simulations for Alternating Automata - (Extended Abstract)
Abstract. We study generalized simulation relations for alternating Büchi automata (ABA), as well as alternating finite automata. Having multiple pebbles allows the Duplicator to “hedge her bets ” and delay decisions in the simulation game, thus yielding a coarser simulation relation. We define (k1, k2)-simulations, with k1/k2 pebbles on the left/right, respectively. This generalizes previous work on ordinary simulation (i.e., (1, 1)-simulation) for nondeterministic Büchi automata (NBA) in [3] and ABA in [4], and (1, k)-simulation for NBA in [2]. We consider direct, delayed and fair simulations. In each case, the (k1, k2)simulations induce a complete lattice of simulations where (1,1)- and (n, n)simulations are the bottom and top element (if the automaton has n states), respectively, and the order is strict. For any fixed k1, k2, the (k1, k2)-simulation implies (ω-)language inclusion and can be computed in polynomial time. Furthermore, quotienting an ABA w.r.t. (1, n)-delayed simulation preserves its language. Finally, multipebble simulations yield new insights into the Miyano-Hayashi construction [10] on ABA.
Bidimensional Linear Recursive Sequences and Universality of Unambiguous Register Automata
We study the universality and inclusion problems for register automata over
equality data. We show that the universality and the inclusion problems can be
solved with 2-EXPTIME complexity when the input automata are without guessing
and unambiguous, improving on the currently best-known 2-EXPSPACE upper bound
by Mottet and Quaas. When the number of registers of both automata is fixed, we
obtain a lower EXPTIME complexity, also improving the EXPSPACE upper bound from
Mottet and Quaas for fixed number of registers. We reduce inclusion to
universality, and then we reduce universality to the problem of counting the
number of orbits of runs of the automaton. We show that the orbit-counting
function satisfies a system of bidimensional linear recursive equations with
polynomial coefficients (linrec), which generalises analogous recurrences for
the Stirling numbers of the second kind, and then we show that universality
reduces to the zeroness problem for linrec sequences. While such a counting
approach is classical and has successfully been applied to unambiguous finite
automata and grammars over finite alphabets, its application to register
automata over infinite alphabets is novel. We provide two algorithms to decide
the zeroness problem for bidimensional linear recursive sequences arising from
orbit-counting functions. Both algorithms rely on techniques from linear
non-commutative algebra. The first algorithm performs variable elimination and
has elementary complexity. The second algorithm is a refined version of the
first one and it relies on the computation of the Hermite normal form of
matrices over a skew polynomial field. The second algorithm yields an EXPTIME
decision procedure for the zeroness problem of linrec sequences, which in turn
yields the claimed bounds for the universality and inclusion problems of
register automata.Comment: full version of the homonymous paper to appear in the proceedings of
STACS'2
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