518 research outputs found
Verification for Timed Automata extended with Unbounded Discrete Data Structures
We study decidability of verification problems for timed automata extended
with unbounded discrete data structures. More detailed, we extend timed
automata with a pushdown stack. In this way, we obtain a strong model that may
for instance be used to model real-time programs with procedure calls. It is
long known that the reachability problem for this model is decidable. The goal
of this paper is to identify subclasses of timed pushdown automata for which
the language inclusion problem and related problems are decidable
Dense-choice Counter Machines revisited
This paper clarifies the picture about Dense-choice Counter Machines, which
have been less studied than (discrete) Counter Machines. We revisit the
definition of "Dense Counter Machines" so that it now extends (discrete)
Counter Machines, and we provide new undecidability and decidability results.
Using the first-order additive mixed theory of reals and integers, we give a
logical characterization of the sets of configurations reachable by
reversal-bounded Dense-choice Counter Machines
Weak Singular Hybrid Automata
The framework of Hybrid automata, introduced by Alur, Courcourbetis,
Henzinger, and Ho, provides a formal modeling and analysis environment to
analyze the interaction between the discrete and the continuous parts of
cyber-physical systems. Hybrid automata can be considered as generalizations of
finite state automata augmented with a finite set of real-valued variables
whose dynamics in each state is governed by a system of ordinary differential
equations. Moreover, the discrete transitions of hybrid automata are guarded by
constraints over the values of these real-valued variables, and enable
discontinuous jumps in the evolution of these variables. Singular hybrid
automata are a subclass of hybrid automata where dynamics is specified by
state-dependent constant vectors. Henzinger, Kopke, Puri, and Varaiya showed
that for even very restricted subclasses of singular hybrid automata, the
fundamental verification questions, like reachability and schedulability, are
undecidable. In this paper we present \emph{weak singular hybrid automata}
(WSHA), a previously unexplored subclass of singular hybrid automata, and show
the decidability (and the exact complexity) of various verification questions
for this class including reachability (NP-Complete) and LTL model-checking
(PSPACE-Complete). We further show that extending WSHA with a single
unrestricted clock or extending WSHA with unrestricted variable updates lead to
undecidability of reachability problem
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
On the Path-Width of Integer Linear Programming
We consider the feasibility problem of integer linear programming (ILP). We
show that solutions of any ILP instance can be naturally represented by an
FO-definable class of graphs. For each solution there may be many graphs
representing it. However, one of these graphs is of path-width at most 2n,
where n is the number of variables in the instance. Since FO is decidable on
graphs of bounded path- width, we obtain an alternative decidability result for
ILP. The technique we use underlines a common principle to prove decidability
which has previously been employed for automata with auxiliary storage. We also
show how this new result links to automata theory and program verification.Comment: In Proceedings GandALF 2014, arXiv:1408.556
- …