230 research outputs found
Parametric Linear Dynamic Logic
We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear
Dynamic Logic (LDL) by temporal operators equipped with parameters that bound
their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL)
that is able to express all -regular specifications while still
maintaining many of LTL's desirable properties like an intuitive syntax and a
translation into non-deterministic B\"uchi automata of exponential size. But
LDL lacks capabilities to express timing constraints. By adding parameterized
operators to LDL, we obtain a logic that is able to express all
-regular properties and that subsumes parameterized extensions of LTL
like Parametric LTL and PROMPT-LTL. Our main technical contribution is a
translation of PLDL formulas into non-deterministic B\"uchi word automata of
exponential size via alternating automata. This yields a PSPACE model checking
algorithm and a realizability algorithm with doubly-exponential running time.
Furthermore, we give tight upper and lower bounds on optimal parameter values
for both problems. These results show that PLDL model checking and
realizability are not harder than LTL model checking and realizability.Comment: In Proceedings GandALF 2014, arXiv:1408.556
MTL-Model Checking of One-Clock Parametric Timed Automata is Undecidable
Parametric timed automata extend timed automata (Alur and Dill, 1991) in that
they allow the specification of parametric bounds on the clock values. Since
their introduction in 1993 by Alur, Henzinger, and Vardi, it is known that the
emptiness problem for parametric timed automata with one clock is decidable,
whereas it is undecidable if the automaton uses three or more parametric
clocks. The problem is open for parametric timed automata with two parametric
clocks. Metric temporal logic, MTL for short, is a widely used specification
language for real-time systems. MTL-model checking of timed automata is
decidable, no matter how many clocks are used in the timed automaton. In this
paper, we prove that MTL-model checking for parametric timed automata is
undecidable, even if the automaton uses only one clock and one parameter and is
deterministic.Comment: In Proceedings SynCoP 2014, arXiv:1403.784
Parameterized Linear Temporal Logics Meet Costs: Still not Costlier than LTL
We continue the investigation of parameterized extensions of Linear Temporal
Logic (LTL) that retain the attractive algorithmic properties of LTL: a
polynomial space model checking algorithm and a doubly-exponential time
algorithm for solving games. Alur et al. and Kupferman et al. showed that this
is the case for Parametric LTL (PLTL) and PROMPT-LTL respectively, which have
temporal operators equipped with variables that bound their scope in time.
Later, this was also shown to be true for Parametric LDL (PLDL), which extends
PLTL to be able to express all omega-regular properties.
Here, we generalize PLTL to systems with costs, i.e., we do not bound the
scope of operators in time, but bound the scope in terms of the cost
accumulated during time. Again, we show that model checking and solving games
for specifications in PLTL with costs is not harder than the corresponding
problems for LTL. Finally, we discuss PLDL with costs and extensions to
multiple cost functions.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Parametric Interval Temporal Logic over Infinite Words
Model checking for Halpern and Shoham’s interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics. Here, we focus on the trace-based semantics, where the infinite execution paths (traces) of the given (finite) Kripke structure are the main semantic entities. In this setting, each finite infix of a trace is interpreted as an interval, and a proposition holds over an interval if and only if it holds over each component state (homogeneity assumption). In this paper, we introduce a quantitative extension of HS over traces, called parametric HS (PHS). The novel logic allows to express parametric timing constraints on the duration (length) of the intervals. We show that checking the existence of a parameter valuation for which a Kripke structure satisfies a PHS formula (model checking), or a PHS formula admits a trace as a model under the homogeneity assumption (satisfiability) is decidable. Moreover, we identify a fragment of PHS which subsumes parametric LTL and for which model checking and satisfiability are shown to be EXPSPACE-complete
Promptness and Bounded Fairness in Concurrent and Parameterized Systems
We investigate the satisfaction of specifications in Prompt
Linear Temporal Logic (Prompt-LTL) by concurrent systems. Prompt-LTL is an extension of LTL that allows to specify parametric bounds onthe satisfaction of eventualities, thus adding a quantitative aspect to the specification language. We establish a connection between bounded fairness, bounded stutter equivalence, and the satisfaction of Prompt-LTL\X
formulas. Based on this connection, we prove the first cutoff results for different classes of systems with a parametric number of components and quantitative specifications, thereby identifying previously unknown
decidable fragments of the parameterized model checking problem
Group synthesis for alternating-time temporal logic
We present an extension of Alternating-time Temporal Logic ATL, called ATLP (Parametric ATL), where parameters are allowed in place of concrete groups of agents. We devise a procedure to nd all instantiations for the parameters in a given formula of ATLP so that is true in a given model. We propose a formalisation of the problem and symbolic algorithms for its solution. We discuss an experimental implementation of the approach on top of the open-source model checker mcmas and demonstrate the bene ts of the technique through experimental results
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