78,151 research outputs found
Interrupt Timed Automata: verification and expressiveness
We introduce the class of Interrupt Timed Automata (ITA), a subclass of
hybrid automata well suited to the description of timed multi-task systems with
interruptions in a single processor environment. While the reachability problem
is undecidable for hybrid automata we show that it is decidable for ITA. More
precisely we prove that the untimed language of an ITA is regular, by building
a finite automaton as a generalized class graph. We then establish that the
reachability problem for ITA is in NEXPTIME and in PTIME when the number of
clocks is fixed. To prove the first result, we define a subclass ITA- of ITA,
and show that (1) any ITA can be reduced to a language-equivalent automaton in
ITA- and (2) the reachability problem in this subclass is in NEXPTIME (without
any class graph). In the next step, we investigate the verification of real
time properties over ITA. We prove that model checking SCL, a fragment of a
timed linear time logic, is undecidable. On the other hand, we give model
checking procedures for two fragments of timed branching time logic. We also
compare the expressive power of classical timed automata and ITA and prove that
the corresponding families of accepted languages are incomparable. The result
also holds for languages accepted by controlled real-time automata (CRTA), that
extend timed automata. We finally combine ITA with CRTA, in a model which
encompasses both classes and show that the reachability problem is still
decidable. Additionally we show that the languages of ITA are neither closed
under complementation nor under intersection
Bayesian Logic Programs
Bayesian networks provide an elegant formalism for representing and reasoning
about uncertainty using probability theory. Theyare a probabilistic extension
of propositional logic and, hence, inherit some of the limitations of
propositional logic, such as the difficulties to represent objects and
relations. We introduce a generalization of Bayesian networks, called Bayesian
logic programs, to overcome these limitations. In order to represent objects
and relations it combines Bayesian networks with definite clause logic by
establishing a one-to-one mapping between ground atoms and random variables. We
show that Bayesian logic programs combine the advantages of both definite
clause logic and Bayesian networks. This includes the separation of
quantitative and qualitative aspects of the model. Furthermore, Bayesian logic
programs generalize both Bayesian networks as well as logic programs. So, many
ideas developedComment: 52 page
Making proofs without Modus Ponens: An introduction to the combinatorics and complexity of cut elimination
This paper is intended to provide an introduction to cut elimination which is
accessible to a broad mathematical audience. Gentzen's cut elimination theorem
is not as well known as it deserves to be, and it is tied to a lot of
interesting mathematical structure. In particular we try to indicate some
dynamical and combinatorial aspects of cut elimination, as well as its
connections to complexity theory. We discuss two concrete examples where one
can see the structure of short proofs with cuts, one concerning feasible
numbers and the other concerning "bounded mean oscillation" from real analysis
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
Logic Programming and Logarithmic Space
We present an algebraic view on logic programming, related to proof theory
and more specifically linear logic and geometry of interaction. Within this
construction, a characterization of logspace (deterministic and
non-deterministic) computation is given via a synctactic restriction, using an
encoding of words that derives from proof theory.
We show that the acceptance of a word by an observation (the counterpart of a
program in the encoding) can be decided within logarithmic space, by reducing
this problem to the acyclicity of a graph. We show moreover that observations
are as expressive as two-ways multi-heads finite automata, a kind of pointer
machines that is a standard model of logarithmic space computation
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