3,495 research outputs found
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
Truly On-The-Fly LTL Model Checking
We propose a novel algorithm for automata-based LTL model checking that
interleaves the construction of the generalized B\"{u}chi automaton for the
negation of the formula and the emptiness check. Our algorithm first converts
the LTL formula into a linear weak alternating automaton; configurations of the
alternating automaton correspond to the locations of a generalized B\"{u}chi
automaton, and a variant of Tarjan's algorithm is used to decide the existence
of an accepting run of the product of the transition system and the automaton.
Because we avoid an explicit construction of the B\"{u}chi automaton, our
approach can yield significant improvements in runtime and memory, for large
LTL formulas. The algorithm has been implemented within the SPIN model checker,
and we present experimental results for some benchmark examples
An Efficient Normalisation Procedure for Linear Temporal Logic and Very Weak Alternating Automata
In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical theorem
stating that every formula of Past LTL (the extension of LTL with past
operators) is equivalent to a formula of the form , where
and contain only past operators. Some years later, Chang,
Manna, and Pnueli built on this result to derive a similar normal form for LTL.
Both normalisation procedures have a non-elementary worst-case blow-up, and
follow an involved path from formulas to counter-free automata to star-free
regular expressions and back to formulas. We improve on both points. We present
a direct and purely syntactic normalisation procedure for LTL yielding a normal
form, comparable to the one by Chang, Manna, and Pnueli, that has only a single
exponential blow-up. As an application, we derive a simple algorithm to
translate LTL into deterministic Rabin automata. The algorithm normalises the
formula, translates it into a special very weak alternating automaton, and
applies a simple determinisation procedure, valid only for these special
automata.Comment: This is the extended version of the referenced conference paper and
contains an appendix with additional materia
Visibly Linear Dynamic Logic
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear
Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown
languages over finite words. In VLDL one can, e.g., express that a function
resets a variable to its original value after its execution, even in the
presence of an unbounded number of intermediate recursive calls. We prove that
VLDL describes exactly the -visibly pushdown languages. Thus it is
strictly more expressive than LTL and able to express recursive properties of
programs with unbounded call stacks.
The main technical contribution of this work is a translation of VLDL into
-visibly pushdown automata of exponential size via one-way alternating
jumping automata. This translation yields exponential-time algorithms for
satisfiability, validity, and model checking. We also show that visibly
pushdown games with VLDL winning conditions are solvable in triply-exponential
time. We prove all these problems to be complete for their respective
complexity classes.Comment: 25 Page
Quantified CTL: Expressiveness and Complexity
While it was defined long ago, the extension of CTL with quantification over
atomic propositions has never been studied extensively. Considering two
different semantics (depending whether propositional quantification refers to
the Kripke structure or to its unwinding tree), we study its expressiveness
(showing in particular that QCTL coincides with Monadic Second-Order Logic for
both semantics) and characterise the complexity of its model-checking and
satisfiability problems, depending on the number of nested propositional
quantifiers (showing that the structure semantics populates the polynomial
hierarchy while the tree semantics populates the exponential hierarchy)
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