Results 1  10
of
74
Optimizations for LTL synthesis
 IN 6TH CONFERENCE ON FORMAL METHODS IN COMPUTER AIDED DESIGN (FMCAD’06
, 2006
"... We present an approach to automatic synthesis of specifications given in Linear Time Logic. The approach is based on a translation through universal coBüchi tree automata and alternating weak tree automata [1]. By careful optimization of all intermediate automata, we achieve a major improvement i ..."
Abstract

Cited by 59 (10 self)
 Add to MetaCart
We present an approach to automatic synthesis of specifications given in Linear Time Logic. The approach is based on a translation through universal coBüchi tree automata and alternating weak tree automata [1]. By careful optimization of all intermediate automata, we achieve a major improvement in performance. We present several optimization techniques for alternating tree automata, including a gamebased approximation to language emptiness and a simulationbased optimization. Furthermore, we use an incremental algorithm to compute the emptiness of nondeterministic Büchi tree automata. All our optimizations are computed in time polynomial in the size of the automaton on which they are computed. We have applied our implementation to several examples and show a significant improvement over the straightforward implementation. Although our examples are still small, this work constitutes the first implementation of a synthesis algorithm for full LTL. We believe that the optimizations discussed here form an important step towards making LTL synthesis practical.
Bounded synthesis
, 2007
"... The bounded synthesis problem is to construct an implementation that satisfies a given temporal specification and a given bound on the number of states. We present a solution to the bounded synthesis problem for lineartime temporal logic (LTL), based on a novel emptinesspreserving translation from ..."
Abstract

Cited by 41 (9 self)
 Add to MetaCart
(Show Context)
The bounded synthesis problem is to construct an implementation that satisfies a given temporal specification and a given bound on the number of states. We present a solution to the bounded synthesis problem for lineartime temporal logic (LTL), based on a novel emptinesspreserving translation from LTL to safety tree automata. For distributed architectures, where standard unbounded synthesis is in general undecidable, we show that bounded synthesis can be reduced to a SAT problem. As a result, we obtain an effective algorithm for the bounded synthesis from LTL specifications in arbitrary architectures. By iteratively increasing the bound, our construction can also be used as a semidecision procedure for the unbounded synthesis problem.
An optimal strategy improvement algorithm for solving parity games
, 2007
"... Abstract. This paper presents a novel strategy improvement algorithm for parity and payoff games, which is guaranteed to select, in each improvement step, an optimal combination of local strategy modifications. Current strategy improvement methods stepwise improve the strategy of one player with res ..."
Abstract

Cited by 30 (1 self)
 Add to MetaCart
(Show Context)
Abstract. This paper presents a novel strategy improvement algorithm for parity and payoff games, which is guaranteed to select, in each improvement step, an optimal combination of local strategy modifications. Current strategy improvement methods stepwise improve the strategy of one player with respect to some ranking function, using an algorithm with two distinct phases: They first choose a modification to the strategy of one player from a list of locally profitable changes, and subsequently evaluate the modified strategy. This separation is unfortunate, because current strategy improvement algorithms have no effective means to predict the global effect of the individual local modifications beyond classifying them as profitable, adversarial, or stale. Furthermore, they are completely blind towards the cross effect of different modifications: Applying one profitable modification may render all other profitable modifications adversarial. Our new construction overcomes the traditional separation between choosing and evaluating the modification to the strategy. It thus improves over current strategy improvement algorithms by providing the optimal improvement in every step, selecting the best combination of local updates from a superset of all profitable and stale changes. 1
Safraless compositional synthesis
 In CAV
, 2006
"... Abstract. In automated synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. In spite of the rich theory developed for system synthesis, little of this theory has been reduced to practice. This is in contrast with of modelchecking theory, which has l ..."
Abstract

Cited by 28 (9 self)
 Add to MetaCart
Abstract. In automated synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. In spite of the rich theory developed for system synthesis, little of this theory has been reduced to practice. This is in contrast with of modelchecking theory, which has led to industrial development and use of formal verification tools. We see two main reasons for the lack of practical impact of synthesis. The first is algorithmic: synthesis involves Safra’s determinization of automata on infinite words, and a solution of parity games with highly complex state spaces; both problems have been notoriously resistant to efficient implementation. The second is methodological: current theory of synthesis assumes a single comprehensive specification. In practice, however, the specification is composed of a set of properties, which is typically evolving – properties may be added, deleted, or modified. In this work we address both issues. We extend the Safraless synthesis algorithm of Kupferman and Vardi so that it handles LTL formulas by translating them to nondeterministic generalized Büchi automata. This leads to an exponential improvement in the complexity of the algorithm. Technically, our algorithm reduces the synthesis problem to the emptiness problem of a nondeterministic Büchi tree automaton A. The generation of A avoids determinization, avoids the parity acceptance condition, and is based on an analysis of runs of universal generalized coBüchi tree automata. The clean and simple structure of A enables optimizations and a symbolic implementation. In addition, it makes it possible to use information gathered during the synthesis process of properties in the process of synthesizing their conjunction. 1
Solving Parity Games in Practice
"... Abstract. Parity games are 2player games of perfect information and infinite duration that have important applications in automata theory and decision procedures (validity as well as model checking) for temporal logics. In this paper we investigate practical aspects of solving parity games. The mai ..."
Abstract

Cited by 27 (9 self)
 Add to MetaCart
(Show Context)
Abstract. Parity games are 2player games of perfect information and infinite duration that have important applications in automata theory and decision procedures (validity as well as model checking) for temporal logics. In this paper we investigate practical aspects of solving parity games. The main contribution is a suggestion on how to solve parity games efficiently in practice: we present a generic solver that intertwines optimisations with any of the existing parity game algorithms which is only called on parts of a game that cannot be solved faster by simpler methods. This approach is evaluated empirically on a series of benchmarking games from the aforementioned application domains, showing that using this approach vastly speeds up the solving process. As a sideeffect we obtain the surprising observation that Zielonka’s recursive algorithm is the best parity game solver in practice. 1
An Antichain Algorithm for LTL Realizability
, 2009
"... In this paper, we study the structure of underlying automata based constructions for solving the LTL realizability and synthesis problem. We show how to reduce the LTL realizability problem to a game with an observer that checks that the game visits a bounded number of times accepting states of a u ..."
Abstract

Cited by 26 (6 self)
 Add to MetaCart
(Show Context)
In this paper, we study the structure of underlying automata based constructions for solving the LTL realizability and synthesis problem. We show how to reduce the LTL realizability problem to a game with an observer that checks that the game visits a bounded number of times accepting states of a universal coBüchi word automaton. We show that such an observer can be made deterministic and that this deterministic observer has a nice structure which can be exploited by an incremental algorithm that manipulates antichains of game positions. We have implemented this new algorithm and our first results are very encouraging.
Environment Assumptions for Synthesis
, 2008
"... The synthesis problem asks to construct a reactive finitestate system from an ωregular specification. Initial specifications are often unrealizable, which means that there is no system that implements the specification. A common reason for unrealizability is that assumptions on the environment of ..."
Abstract

Cited by 25 (4 self)
 Add to MetaCart
(Show Context)
The synthesis problem asks to construct a reactive finitestate system from an ωregular specification. Initial specifications are often unrealizable, which means that there is no system that implements the specification. A common reason for unrealizability is that assumptions on the environment of the system are incomplete. We study the problem of correcting an unrealizable specification ϕ by computing an environment assumption ψ such that the new specification ψ → ϕ is realizable. Our aim is to construct an assumption ψ that constrains only the environment and is as weak as possible. We present a twostep algorithm for computing assumptions. The algorithm operates on the game graph that is used to answer the realizability question. First, we compute a safety assumption that removes a minimal set of environment edges from the graph. Second, we compute a liveness assumption that puts fairness conditions on some of the remaining environment edges. We show that the problem of finding a minimal set of fair edges is computationally hard, and we use probabilistic games to compute a locally minimal fairness assumption.
Tighter bounds for the determinisation of Büchi automata
 In FoSSaCS 09
, 2009
"... Abstract. The introduction of an eÆcient determinisation technique for Buchi automata by Safra has been a milestone in automata theory. To name only a few applications, eÆcient determinisation techniques for!word automata are the basis for several manipulations of!tree automata (most prominently t ..."
Abstract

Cited by 21 (5 self)
 Add to MetaCart
(Show Context)
Abstract. The introduction of an eÆcient determinisation technique for Buchi automata by Safra has been a milestone in automata theory. To name only a few applications, eÆcient determinisation techniques for!word automata are the basis for several manipulations of!tree automata (most prominently the nondeterminisation of alternating tree automata) as well as for satisability checking and model synthesis for branching and alternatingtime logics. This paper proposes a determinisation technique that is simpler than the constructions of Safra, Piterman, and Muller and Schupp, because it separates the principle acceptance mechanism from the concrete acceptance condition. The principle mechanism intuitively uses a Rabin condition on the transitions; we show how to obtain an equivalent Rabin transition automaton with approximately (1:65 n) n states from a nondeterministic Buchi automaton with n states. Having established this mechanism, it is simple to develop translations to automata with standard acceptance conditions. We can construct standard Rabin automata whose statespace is bilinear in the size of the input alphabet and the statespace of the Rabin transition automaton, or, for large input alphabets, contains approximately (2:66 n) n states, respectively. We also provide a
exible translation to parity automata with O(n! 2) states and 2n priorities based on a later introduction record, and hence connect the transformation of the acceptance condition to other record based transformations known from the literature. 1
BÜCHI COMPLEMENTATION MADE TIGHT
, 2009
"... The precise complexity of complementing Büchi automata is an intriguing and long standing problem. While optimal complementation techniques for finite automata are simple – it suffices to determinize them using a simple subset construction and to dualize the acceptance condition of the resulting au ..."
Abstract

Cited by 20 (4 self)
 Add to MetaCart
The precise complexity of complementing Büchi automata is an intriguing and long standing problem. While optimal complementation techniques for finite automata are simple – it suffices to determinize them using a simple subset construction and to dualize the acceptance condition of the resulting automaton – Büchi complementation is more involved. Indeed, the construction of an EXPTIME complementation procedure took a quarter of a century from the introduction of Büchi automata in the early 60s, and stepwise narrowing the gap between the upper and lower bound to a simple exponent (of (6e) n for Büchi automata with n states) took four decades. While the distance between the known upper (O ` (0.96 n) n ´ ) and lower (Ω ` (0.76 n) n ´ ) bound on the required number of states has meanwhile been significantly reduced, an exponential factor remains between them. Also, the upper bound on the size of the complement automaton is not linear in the bound of its state space. These gaps are unsatisfactory from a theoretical point of view, but also because Büchi complementation is a useful tool in formal verification, in particular for the language containment problem. This paper proposes a Büchi complementation algorithm whose complexity meets, modulo a quadratic (O(n 2)) factor, the known lower bound for Büchi complementation. It thus improves over previous constructions by an exponential factor and concludes the quest for optimal Büchi complementation algorithms.