3,540 research outputs found
Mightyl: A compositional translation from mitl to timed automata
Metric Interval Temporal Logic (MITL) was first proposed in the early 1990s as a specification formalism for real-time systems. Apart from its appealing intuitive syntax, there are also theoretical evidences that make MITL a prime real-time counterpart of Linear Temporal Logic (LTL). Unfortunately, the tool support for MITL verification is still lacking to this day. In this paper, we propose a new construction from MITL to timed automata via very-weak one-clock alternating timed automata. Our construction subsumes the well-known construction from LTL to BĂĽchi automata by Gastin and Oddoux and yet has the additional benefits of being compositional and integrating easily with existing tools. We implement the construction in our new tool MightyL and report on experiments using Uppaal and LTSmin as back-ends
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
Separation Property for wB- and wS-regular Languages
In this paper we show that {\omega}B- and {\omega}S-regular languages satisfy
the following separation-type theorem If L1,L2 are disjoint languages of
{\omega}-words both recognised by {\omega}B- (resp. {\omega}S)-automata then
there exists an {\omega}-regular language Lsep that contains L1, and whose
complement contains L2. In particular, if a language and its complement are
recognised by {\omega}B- (resp. {\omega}S)-automata then the language is
{\omega}-regular. The result is especially interesting because, as shown by
Boja\'nczyk and Colcombet, {\omega}B-regular languages are complements of
{\omega}S-regular languages. Therefore, the above theorem shows that these are
two mutually dual classes that both have the separation property. Usually (e.g.
in descriptive set theory or recursion theory) exactly one class from a pair C,
Cc has the separation property. The proof technique reduces the separation
property for {\omega}-word languages to profinite languages using Ramsey's
theorem and topological methods. After that reduction, the analysis of the
separation property in the profinite monoid is relatively simple. The whole
construction is technically not complicated, moreover it seems to be quite
extensible. The paper uses a framework for the analysis of B- and S-regular
languages in the context of the profinite monoid that was proposed by
Toru\'nczyk
Multi-Player Games with LDL Goals over Finite Traces
Linear Dynamic Logic on finite traces LDLf is a powerful logic for reasoning
about the behaviour of concurrent and multi-agent systems.
In this paper, we investigate techniques for both the characterisation and
verification of equilibria in multi-player games with goals/objectives
expressed using logics based on LDLf. This study builds upon a generalisation
of Boolean games, a logic-based game model of multi-agent systems where players
have goals succinctly represented in a logical way.
Because LDLf goals are considered, in the settings we study -- Reactive
Modules games and iterated Boolean games with goals over finite traces --
players' goals can be defined to be regular properties while achieved in a
finite, but arbitrarily large, trace.
In particular, using alternating automata, the paper investigates
automata-theoretic approaches to the characterisation and verification of (pure
strategy Nash) equilibria, shows that the set of Nash equilibria in
multi-player games with LDLf objectives is regular, and provides complexity
results for the associated automata constructions
Multi-player games with LDL goals over finite traces
Linear Dynamic Logic on finite traces (LDLF) is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in multi-player games with goals/objectives expressed using logics based on LDLF. This study builds upon a generalisation of Boolean games, a logic-based game model of multi-agent systems where players have goals succinctly represented in a logical way. Because LDLF goals are considered, in the settings we study—Reactive Modules games and iterated Boolean games with goals over finite traces—players' goals can be defined to be regular properties while achieved in a finite, but arbitrarily large, trace. In particular, using alternating automata, the paper investigates automata-theoretic approaches to the characterisation and verification of (pure strategy Nash) equilibria, shows that the set of Nash equilibria in multi-player games with LDLF objectives is regular, and provides complexity results for the associated automata constructions
Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis
The classic approaches to synthesize a reactive system from a linear temporal
logic (LTL) specification first translate the given LTL formula to an
equivalent omega-automaton and then compute a winning strategy for the
corresponding omega-regular game. To this end, the obtained omega-automata have
to be (pseudo)-determinized where typically a variant of Safra's
determinization procedure is used. In this paper, we show that this
determinization step can be significantly improved for tool implementations by
replacing Safra's determinization by simpler determinization procedures. In
particular, we exploit (1) the temporal logic hierarchy that corresponds to the
well-known automata hierarchy consisting of safety, liveness, Buechi, and
co-Buechi automata as well as their boolean closures, (2) the non-confluence
property of omega-automata that result from certain translations of LTL
formulas, and (3) symbolic implementations of determinization procedures for
the Rabin-Scott and the Miyano-Hayashi breakpoint construction. In particular,
we present convincing experimental results that demonstrate the practical
applicability of our new synthesis procedure
Bounds on the Automata Size for Presburger Arithmetic
Automata provide a decision procedure for Presburger arithmetic. However,
until now only crude lower and upper bounds were known on the sizes of the
automata produced by this approach. In this paper, we prove an upper bound on
the the number of states of the minimal deterministic automaton for a
Presburger arithmetic formula. This bound depends on the length of the formula
and the quantifiers occurring in the formula. The upper bound is established by
comparing the automata for Presburger arithmetic formulas with the formulas
produced by a quantifier elimination method. We also show that our bound is
tight, even for nondeterministic automata. Moreover, we provide optimal
automata constructions for linear equations and inequations
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+
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