533 research outputs found
One Theorem to Rule Them All: A Unified Translation of LTL into {\omega}-Automata
We present a unified translation of LTL formulas into deterministic Rabin
automata, limit-deterministic B\"uchi automata, and nondeterministic B\"uchi
automata. The translations yield automata of asymptotically optimal size
(double or single exponential, respectively). All three translations are
derived from one single Master Theorem of purely logical nature. The Master
Theorem decomposes the language of a formula into a positive boolean
combination of languages that can be translated into {\omega}-automata by
elementary means. In particular, Safra's, ranking, and breakpoint constructions
used in other translations are not needed
Constraint LTL Satisfiability Checking without Automata
This paper introduces a novel technique to decide the satisfiability of
formulae written in the language of Linear Temporal Logic with Both future and
past operators and atomic formulae belonging to constraint system D (CLTLB(D)
for short). The technique is based on the concept of bounded satisfiability,
and hinges on an encoding of CLTLB(D) formulae into QF-EUD, the theory of
quantifier-free equality and uninterpreted functions combined with D. Similarly
to standard LTL, where bounded model-checking and SAT-solvers can be used as an
alternative to automata-theoretic approaches to model-checking, our approach
allows users to solve the satisfiability problem for CLTLB(D) formulae through
SMT-solving techniques, rather than by checking the emptiness of the language
of a suitable automaton A_{\phi}. The technique is effective, and it has been
implemented in our Zot formal verification tool.Comment: 39 page
Near-Optimal Scheduling for LTL with Future Discounting
We study the search problem for optimal schedulers for the linear temporal
logic (LTL) with future discounting. The logic, introduced by Almagor, Boker
and Kupferman, is a quantitative variant of LTL in which an event in the far
future has only discounted contribution to a truth value (that is a real number
in the unit interval [0, 1]). The precise problem we study---it naturally
arises e.g. in search for a scheduler that recovers from an internal error
state as soon as possible---is the following: given a Kripke frame, a formula
and a number in [0, 1] called a margin, find a path of the Kripke frame that is
optimal with respect to the formula up to the prescribed margin (a truly
optimal path may not exist). We present an algorithm for the problem; it works
even in the extended setting with propositional quality operators, a setting
where (threshold) model-checking is known to be undecidable
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 Büchi 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
Conditionally Optimal Algorithms for Generalized B\"uchi Games
Games on graphs provide the appropriate framework to study several central
problems in computer science, such as the verification and synthesis of
reactive systems. One of the most basic objectives for games on graphs is the
liveness (or B\"uchi) objective that given a target set of vertices requires
that some vertex in the target set is visited infinitely often. We study
generalized B\"uchi objectives (i.e., conjunction of liveness objectives), and
implications between two generalized B\"uchi objectives (known as GR(1)
objectives), that arise in numerous applications in computer-aided
verification. We present improved algorithms and conditional super-linear lower
bounds based on widely believed assumptions about the complexity of (A1)
combinatorial Boolean matrix multiplication and (A2) CNF-SAT. We consider graph
games with vertices, edges, and generalized B\"uchi objectives with
conjunctions. First, we present an algorithm with running time , improving the previously known and worst-case bounds. Our algorithm is optimal for dense graphs under (A1).
Second, we show that the basic algorithm for the problem is optimal for sparse
graphs when the target sets have constant size under (A2). Finally, we consider
GR(1) objectives, with conjunctions in the antecedent and
conjunctions in the consequent, and present an -time algorithm, improving the previously known -time algorithm for
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
Prompt Delay
Delay games are two-player games of infinite duration in which one player may
delay her moves to obtain a lookahead on her opponent's moves. Recently, such
games with quantitative winning conditions in weak MSO with the unbounding
quantifier were studied, but their properties turned out to be unsatisfactory.
In particular, unbounded lookahead is in general necessary. Here, we study
delay games with winning conditions given by Prompt-LTL, Linear Temporal Logic
equipped with a parameterized eventually operator whose scope is bounded. Our
main result shows that solving Prompt-LTL delay games is complete for
triply-exponential time. Furthermore, we give tight triply-exponential bounds
on the necessary lookahead and on the scope of the parameterized eventually
operator. Thus, we identify Prompt-LTL as the first known class of well-behaved
quantitative winning conditions for delay games. Finally, we show that applying
our techniques to delay games with \omega-regular winning conditions answers
open questions in the cases where the winning conditions are given by
non-deterministic, universal, or alternating automata
Coalgebraic Trace Semantics for Buechi and Parity Automata
Despite its success in producing numerous general results on state-based dynamics, the theory of coalgebra has struggled to accommodate the Buechi acceptance condition---a basic notion in the
theory of automata for infinite words or trees. In this paper we present a clean answer to the question that builds on the "maximality" characterization of infinite traces (by Jacobs and Cirstea): the accepted language of a Buechi automaton is characterized by two commuting diagrams, one for a least homomorphism and the other for a greatest, much like in a system of (least and greatest) fixed-point equations. This characterization works uniformly for the nondeterministic branching and the probabilistic one; and for words and trees alike. We present our results in terms of the parity acceptance condition that generalizes Buechi\u27s
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