2,458 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
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
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
Satisfiability Games for Branching-Time Logics
The satisfiability problem for branching-time temporal logics like CTL*, CTL
and CTL+ has important applications in program specification and verification.
Their computational complexities are known: CTL* and CTL+ are complete for
doubly exponential time, CTL is complete for single exponential time. Some
decision procedures for these logics are known; they use tree automata,
tableaux or axiom systems. In this paper we present a uniform game-theoretic
framework for the satisfiability problem of these branching-time temporal
logics. We define satisfiability games for the full branching-time temporal
logic CTL* using a high-level definition of winning condition that captures the
essence of well-foundedness of least fixpoint unfoldings. These winning
conditions form formal languages of \omega-words. We analyse which kinds of
deterministic {\omega}-automata are needed in which case in order to recognise
these languages. We then obtain a reduction to the problem of solving parity or
B\"uchi games. The worst-case complexity of the obtained algorithms matches the
known lower bounds for these logics. This approach provides a uniform, yet
complexity-theoretically optimal treatment of satisfiability for branching-time
temporal logics. It separates the use of temporal logic machinery from the use
of automata thus preserving a syntactical relationship between the input
formula and the object that represents satisfiability, i.e. a winning strategy
in a parity or B\"uchi game. The games presented here work on a Fischer-Ladner
closure of the input formula only. Last but not least, the games presented here
come with an attempt at providing tool support for the satisfiability problem
of complex branching-time logics like CTL* and CTL+
IMITATOR II: A Tool for Solving the Good Parameters Problem in Timed Automata
We present here Imitator II, a new version of Imitator, a tool implementing
the "inverse method" for parametric timed automata: given a reference valuation
of the parameters, it synthesizes a constraint such that, for any valuation
satisfying this constraint, the system behaves the same as under the reference
valuation in terms of traces, i.e., alternating sequences of locations and
actions. Imitator II also implements the "behavioral cartography algorithm",
allowing us to solve the following good parameters problem: find a set of
valuations within a given bounded parametric domain for which the system
behaves well. We present new features and optimizations of the tool, and give
results of applications to various examples of asynchronous circuits and
communication protocols.Comment: In Proceedings INFINITY 2010, arXiv:1010.611
Analysing oscillatory trends of discrete-state stochastic processes through HASL statistical model checking
The application of formal methods to the analysis of stochastic oscillators
has been at the focus of several research works in recent times. In this paper
we provide insights on the application of an expressive temporal logic
formalism, namely the Hybrid Automata Stochastic Logic (HASL), to that issue.
We show how one can take advantage of the expressive power of the HASL logic to
define and assess relevant characteristics of (stochastic) oscillators
Disjunctive form and the modal alternation hierarchy
This paper studies the relationship between disjunctive form, a syntactic
normal form for the modal mu calculus, and the alternation hierarchy. First it
shows that all disjunctive formulas which have equivalent tableau have the same
syntactic alternation depth. However, tableau equivalence only preserves
alternation depth for the disjunctive fragment: there are disjunctive formulas
with arbitrarily high alternation depth that are tableau equivalent to
alternation-free non-disjunctive formulas. Conversely, there are
non-disjunctive formulas of arbitrarily high alternation depth that are tableau
equivalent to disjunctive formulas without alternations. This answers
negatively the so far open question of whether disjunctive form preserves
alternation depth. The classes of formulas studied here illustrate a previously
undocumented type of avoidable syntactic complexity which may contribute to our
understanding of why deciding the alternation hierarchy is still an open
problem.Comment: In Proceedings FICS 2015, arXiv:1509.0282
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