1,979 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
Decidability of the interval temporal logic ABBar over the natural numbers
In this paper, we focus our attention on the interval temporal logic of the
Allen's relations "meets", "begins", and "begun by" (ABBar for short),
interpreted over natural numbers. We first introduce the logic and we show that
it is expressive enough to model distinctive interval properties,such as
accomplishment conditions, to capture basic modalities of point-based temporal
logic, such as the until operator, and to encode relevant metric constraints.
Then, we prove that the satisfiability problem for ABBar over natural numbers
is decidable by providing a small model theorem based on an original
contraction method. Finally, we prove the EXPSPACE-completeness of the proble
On the decidability and complexity of Metric Temporal Logic over finite words
Metric Temporal Logic (MTL) is a prominent specification formalism for
real-time systems. In this paper, we show that the satisfiability problem for
MTL over finite timed words is decidable, with non-primitive recursive
complexity. We also consider the model-checking problem for MTL: whether all
words accepted by a given Alur-Dill timed automaton satisfy a given MTL
formula. We show that this problem is decidable over finite words. Over
infinite words, we show that model checking the safety fragment of MTL--which
includes invariance and time-bounded response properties--is also decidable.
These results are quite surprising in that they contradict various claims to
the contrary that have appeared in the literature
The intuitionistic temporal logic of dynamical systems
A dynamical system is a pair , where is a topological space and
is continuous. Kremer observed that the language of
propositional linear temporal logic can be interpreted over the class of
dynamical systems, giving rise to a natural intuitionistic temporal logic. We
introduce a variant of Kremer's logic, which we denote , and show
that it is decidable. We also show that minimality and Poincar\'e recurrence
are both expressible in the language of , thus providing a
decidable logic expressive enough to reason about non-trivial asymptotic
behavior in dynamical systems
Undecidable First-Order Theories of Affine Geometries
Tarski initiated a logic-based approach to formal geometry that studies
first-order structures with a ternary betweenness relation (\beta) and a
quaternary equidistance relation (\equiv). Tarski established, inter alia, that
the first-order (FO) theory of (R^2,\beta,\equiv) is decidable. Aiello and van
Benthem (2002) conjectured that the FO-theory of expansions of (R^2,\beta) with
unary predicates is decidable. We refute this conjecture by showing that for
all n>1, the FO-theory of monadic expansions of (R^2,\beta) is \Pi^1_1-hard and
therefore not even arithmetical. We also define a natural and comprehensive
class C of geometric structures (T,\beta), where T is a subset of R^2, and show
that for each structure (T,\beta) in C, the FO-theory of the class of monadic
expansions of (T,\beta) is undecidable. We then consider classes of expansions
of structures (T,\beta) with restricted unary predicates, for example finite
predicates, and establish a variety of related undecidability results. In
addition to decidability questions, we briefly study the expressivity of
universal MSO and weak universal MSO over expansions of (R^n,\beta). While the
logics are incomparable in general, over expansions of (R^n,\beta), formulae of
weak universal MSO translate into equivalent formulae of universal MSO.
This is an extended version of a publication in the proceedings of the 21st
EACSL Annual Conferences on Computer Science Logic (CSL 2012).Comment: 21 pages, 3 figure
Temporalized logics and automata for time granularity
Suitable extensions of the monadic second-order theory of k successors have
been proposed in the literature to capture the notion of time granularity. In
this paper, we provide the monadic second-order theories of downward unbounded
layered structures, which are infinitely refinable structures consisting of a
coarsest domain and an infinite number of finer and finer domains, and of
upward unbounded layered structures, which consist of a finest domain and an
infinite number of coarser and coarser domains, with expressively complete and
elementarily decidable temporal logic counterparts.
We obtain such a result in two steps. First, we define a new class of
combined automata, called temporalized automata, which can be proved to be the
automata-theoretic counterpart of temporalized logics, and show that relevant
properties, such as closure under Boolean operations, decidability, and
expressive equivalence with respect to temporal logics, transfer from component
automata to temporalized ones. Then, we exploit the correspondence between
temporalized logics and automata to reduce the task of finding the temporal
logic counterparts of the given theories of time granularity to the easier one
of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym:
TPLP Category: Paper for Special Issue (Verification and Computational Logic)
Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September
200
Weak Alternating Timed Automata
Alternating timed automata on infinite words are considered. The main result
is a characterization of acceptance conditions for which the emptiness problem
for these automata is decidable. This result implies new decidability results
for fragments of timed temporal logics. It is also shown that, unlike for MITL,
the characterisation remains the same even if no punctual constraints are
allowed
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