73,658 research outputs found
Path Checking for MTL and TPTL over Data Words
Metric temporal logic (MTL) and timed propositional temporal logic (TPTL) are
quantitative extensions of linear temporal logic, which are prominent and
widely used in the verification of real-timed systems. It was recently shown
that the path checking problem for MTL, when evaluated over finite timed words,
is in the parallel complexity class NC. In this paper, we derive precise
complexity results for the path-checking problem for MTL and TPTL when
evaluated over infinite data words over the non-negative integers. Such words
may be seen as the behaviours of one-counter machines. For this setting, we
give a complete analysis of the complexity of the path-checking problem
depending on the number of register variables and the encoding of constraint
numbers (unary or binary). As the two main results, we prove that the
path-checking problem for MTL is P-complete, whereas the path-checking problem
for TPTL is PSPACE-complete. The results yield the precise complexity of model
checking deterministic one-counter machines against formulae of MTL and TPTL
A Temporal Logic for Hyperproperties
Hyperproperties, as introduced by Clarkson and Schneider, characterize the
correctness of a computer program as a condition on its set of computation
paths. Standard temporal logics can only refer to a single path at a time, and
therefore cannot express many hyperproperties of interest, including
noninterference and other important properties in security and coding theory.
In this paper, we investigate an extension of temporal logic with explicit path
variables. We show that the quantification over paths naturally subsumes other
extensions of temporal logic with operators for information flow and knowledge.
The model checking problem for temporal logic with path quantification is
decidable. For alternation depth 1, the complexity is PSPACE in the length of
the formula and NLOGSPACE in the size of the system, as for linear-time
temporal logic
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
Symbolic model-checking for resource-bounded ATL
In this paper we present a symbolic implementation of a model
checking algorithm for the verification of properties expressed in
Resource-Bounded Alternating Time Temporal Logic (RB-ATL).
The implementation is based on the model checker MCMAS. We
evaluate the performance of our implementation using simple multi-
agent model checking problems of increasing complexity
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
Counting LTL
The original publication is available at ieeexplore.ieee.org.International audienceThis paper presents a quantitative extension for the linear-time temporal logic LTL allowing to specify the number of states satisfying certain sub-formulas along paths. We give decision procedures for the satisfiability and model checking of this new temporal logic and study the complexity of the corresponding problems. Furthermore we show that the problems become undecidable when more expressive constraints are considered
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