1,311 research outputs found
Syntactic Complexity of Circular Semi-Flower Automata
We investigate the syntactic complexity of certain types of finitely
generated submonoids of a free monoid. In fact, we consider those submonoids
which are accepted by circular semi-flower automata (CSFA). Here, we show that
the syntactic complexity of CSFA with at most one `branch point going in' (bpi)
is linear. Further, we prove that the syntactic complexity of -state CSFA
with two bpis over a binary alphabet is
On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases
This article studies the expressive power of finite automata recognizing sets
of real numbers encoded in positional notation. We consider Muller automata as
well as the restricted class of weak deterministic automata, used as symbolic
set representations in actual applications. In previous work, it has been
established that the sets of numbers that are recognizable by weak
deterministic automata in two bases that do not share the same set of prime
factors are exactly those that are definable in the first order additive theory
of real and integer numbers. This result extends Cobham's theorem, which
characterizes the sets of integer numbers that are recognizable by finite
automata in multiple bases.
In this article, we first generalize this result to multiplicatively
independent bases, which brings it closer to the original statement of Cobham's
theorem. Then, we study the sets of reals recognizable by Muller automata in
two bases. We show with a counterexample that, in this setting, Cobham's
theorem does not generalize to multiplicatively independent bases. Finally, we
prove that the sets of reals that are recognizable by Muller automata in two
bases that do not share the same set of prime factors are exactly those
definable in the first order additive theory of real and integer numbers. These
sets are thus also recognizable by weak deterministic automata. This result
leads to a precise characterization of the sets of real numbers that are
recognizable in multiple bases, and provides a theoretical justification to the
use of weak automata as symbolic representations of sets.Comment: 17 page
On decidability and tractability of querying in temporal EL
We study access to temporal data with TEL, a temporal extension of the tractable description logic EL. Our aim is to establish a clear computational complexity landscape for the atomic query answering problem, in terms of both data and combined complexity. Atomic queries in full TEL turn out to be undecidable even in data complexity. Motivated by the negative result, we identify well-behaved yet expressive fragments of TEL. Our main contributions are a semantic and sufficient syntactic conditions for decidability and three orthogonal tractable fragments, which are based on restricted use of rigid roles, temporal operators, and novel acyclicity conditions on the ontologies
Ambiguity, Weakness, and Regularity in Probabilistic B\"uchi Automata
Probabilistic B\"uchi automata are a natural generalization of PFA to
infinite words, but have been studied in-depth only rather recently and many
interesting questions are still open. PBA are known to accept, in general, a
class of languages that goes beyond the regular languages. In this work we
extend the known classes of restricted PBA which are still regular, strongly
relying on notions concerning ambiguity in classical omega-automata.
Furthermore, we investigate the expressivity of the not yet considered but
natural class of weak PBA, and we also show that the regularity problem for
weak PBA is undecidable
Ultimate periodicity problem for linear numeration systems
We address the following decision problem. Given a numeration system U and a U-recognizable subset X of N, i.e. the set of its greedy U-representations is recognized by a finite automaton, decide whether or not X is ultimately periodic. We prove that this problem is decidable for a large class of numeration systems built on linear recurrence sequences. Based on arithmetical considerations about the recurrence equation and on p-adic methods, the DFA given as input provides a bound on the admissible periods to test
Linear Temporal Logic and Propositional Schemata, Back and Forth (extended version)
This paper relates the well-known Linear Temporal Logic with the logic of
propositional schemata introduced by the authors. We prove that LTL is
equivalent to a class of schemata in the sense that polynomial-time reductions
exist from one logic to the other. Some consequences about complexity are
given. We report about first experiments and the consequences about possible
improvements in existing implementations are analyzed.Comment: Extended version of a paper submitted at TIME 2011: contains proofs,
additional examples & figures, additional comparison between classical
LTL/schemata algorithms up to the provided translations, and an example of
how to do model checking with schemata; 36 pages, 8 figure
A simple abstraction of arrays and maps by program translation
We present an approach for the static analysis of programs handling arrays,
with a Galois connection between the semantics of the array program and
semantics of purely scalar operations. The simplest way to implement it is by
automatic, syntactic transformation of the array program into a scalar program
followed analysis of the scalar program with any static analysis technique
(abstract interpretation, acceleration, predicate abstraction,.. .). The
scalars invariants thus obtained are translated back onto the original program
as universally quantified array invariants. We illustrate our approach on a
variety of examples, leading to the " Dutch flag " algorithm
How hard is it to verify flat affine counter systems with the finite monoid property ?
We study several decision problems for counter systems with guards defined by
convex polyhedra and updates defined by affine transformations. In general, the
reachability problem is undecidable for such systems. Decidability can be
achieved by imposing two restrictions: (i) the control structure of the counter
system is flat, meaning that nested loops are forbidden, and (ii) the set of
matrix powers is finite, for any affine update matrix in the system. We provide
tight complexity bounds for several decision problems of such systems, by
proving that reachability and model checking for Past Linear Temporal Logic are
complete for the second level of the polynomial hierarchy , while
model checking for First Order Logic is PSPACE-complete
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