632 research outputs found
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
On the decidability and complexity of the structural congruence for beta-binders
AbstractBeta-binders is a recent process calculus developed for modelling and simulating biological systems. As usual for process calculi, the semantic definition heavily relies on a structural congruence. The treatment of the structural congruence is essential for implementation. We present a subset of the calculus for which the structural congruence is decidable and a subset for which it is also efficiently solvable. The obtained results are a first step towards implementations
Clausal Resolution for Modal Logics of Confluence
We present a clausal resolution-based method for normal multimodal logics of
confluence, whose Kripke semantics are based on frames characterised by
appropriate instances of the Church-Rosser property. Here we restrict attention
to eight families of such logics. We show how the inference rules related to
the normal logics of confluence can be systematically obtained from the
parametrised axioms that characterise such systems. We discuss soundness,
completeness, and termination of the method. In particular, completeness can be
modularly proved by showing that the conclusions of each newly added inference
rule ensures that the corresponding conditions on frames hold. Some examples
are given in order to illustrate the use of the method.Comment: 15 pages, 1 figure. Preprint of the paper accepted to IJCAR 201
08271 Abstracts Collection -- Topological and Game-Theoretic Aspects of Infinite Computations
From June 29, 2008, to July 4, 2008, the Dagstuhl Seminar 08271 ``Topological and Game-Theoretic Aspects of Infinite Computations\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, many participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available
On Expressiveness of Halpern-Shoham Logic and its Horn Fragments
Abstract: Halpern and Shoham\u27s modal logic of time intervals (HS in short) is an elegant and highly influential propositional interval-based logic. Its Horn fragments and their hybrid extensions have been recently intensively studied and successfully applied in real-world use cases. Detailed investigation of their decidability and computational complexity has been conducted, however, there has been significantly less research on their expressive power. In this paper we make a step towards filling this gap. We (1) show what time structures are definable in the language of HS, and (2) determine which HS fragments are capable of expressing: hybrid machinery, i.e., nominals and satisfaction operators, and somewhere, difference, and everywhere modal operators. These results enable us to classify HS Horn fragments according to their expressive power and to gain insight in the interplay between their decidability/computational complexity and expressiveness
Register automata with linear arithmetic
We propose a novel automata model over the alphabet of rational numbers,
which we call register automata over the rationals (RA-Q). It reads a sequence
of rational numbers and outputs another rational number. RA-Q is an extension
of the well-known register automata (RA) over infinite alphabets, which are
finite automata equipped with a finite number of registers/variables for
storing values. Like in the standard RA, the RA-Q model allows both equality
and ordering tests between values. It, moreover, allows to perform linear
arithmetic between certain variables. The model is quite expressive: in
addition to the standard RA, it also generalizes other well-known models such
as affine programs and arithmetic circuits.
The main feature of RA-Q is that despite the use of linear arithmetic, the
so-called invariant problem---a generalization of the standard non-emptiness
problem---is decidable. We also investigate other natural decision problems,
namely, commutativity, equivalence, and reachability. For deterministic RA-Q,
commutativity and equivalence are polynomial-time inter-reducible with the
invariant problem
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