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83
From nondeterministic Büchi and Streett automata to deterministic parity automata
 In 21st Symposium on Logic in Computer Science (LICS’06
, 2006
"... Determinization and complementation are fundamental notions in computer science. When considering finite automata on finite words determinization gives also a solution to complementation. Given a nondeterministic finite automaton there exists an exponential construction that gives a deterministic au ..."
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Cited by 74 (5 self)
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Determinization and complementation are fundamental notions in computer science. When considering finite automata on finite words determinization gives also a solution to complementation. Given a nondeterministic finite automaton there exists an exponential construction that gives a deterministic automaton for the same language. Dualizing the set of accepting states gives an automaton for the complement language. In the theory of automata on infinite words, determinization and complementation are much more involved. Safra provides determinization constructions for Büchi and Streett automata that result in deterministic Rabin automata. For a Büchi automaton with n states, Safra constructs a deterministic Rabin automaton with n O(n) states and n pairs. For a Streett automaton with n states and k pairs, Safra constructs a deterministic Rabin automaton with (nk) O(nk) states and n(k + 1) pairs. Here, we reconsider Safra’s determinization constructions. We show how to construct automata with fewer states and, most importantly, parity acceptance condition. Specifically, starting from a nondeterministic Büchi automaton with n states our construction yields a deterministic parity automaton with n 2n+2 states and index 2n (instead of a Rabin automaton with (12) n n 2n states and n pairs). Starting from a nondeterministic Streett automaton with n states and k pairs our construction yields a deterministic parity automaton with n n(k+2)+2 (k+1) 2n(k+1) states and index 2n(k + 1) (instead of a Rabin automaton with (12) n(k+1) n n(k+2) (k+1) 2n(k+1) states and n(k+1) pairs). The parity condition is much simpler than the Rabin condition. In applications such as solving games and emptiness of tree automata handling the Rabin condition involves an additional multiplier of n 2 n! (or (n(k + 1)) 2 (n(k + 1))! in the case of Streett) which is saved using our construction.
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 ..."
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Cited by 59 (10 self)
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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 ..."
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Cited by 41 (9 self)
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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.
Automatic synthesis of new behaviors from a library of available behaviors
 In Proc. of IJCAI 2007
, 2007
"... We consider the problem of synthesizing a fully controllable target behavior from a set of available partially controllable behaviors that are to execute within a shared partially predictable, but fully observable, environment. Behaviors are represented with a sort of nondeterministic transition sys ..."
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Cited by 36 (16 self)
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We consider the problem of synthesizing a fully controllable target behavior from a set of available partially controllable behaviors that are to execute within a shared partially predictable, but fully observable, environment. Behaviors are represented with a sort of nondeterministic transition systems, whose transitions are conditioned on the current state of the environment, also represented as a nondeterministic finite transition system. On the other hand, the target behavior is assumed to be fully deterministic and stands for the behavior that the system as a whole needs to guarantee. We formally define the problem within an abstract framework, characterize its computational complexity, and propose a solution by appealing to satisfiability in Propositional Dynamic Logic, which is indeed optimal with respect to computational complexity. We claim that this problem, while novel to the best of our knowledge, can be instantiated to multiple specific settings in different contexts and can thus be linked to different research areas of AI, including agentoriented programming and cognitive robotics, control, multiagent coordination, plan integration, and automatic webservice composition. 1
Synthesis from Component Libraries
"... Synthesis is the automated construction of a system from its specification. In the classical temporal synthesis algorithms, it is always assumed the system is “constructed from scratch” rather than “composed” from reusable components. This, of course, rarely happens in real life. In real life, almos ..."
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Cited by 30 (4 self)
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Synthesis is the automated construction of a system from its specification. In the classical temporal synthesis algorithms, it is always assumed the system is “constructed from scratch” rather than “composed” from reusable components. This, of course, rarely happens in real life. In real life, almost every nontrivial commercial system, either in hardware or in software system, relies heavily on using libraries of reusable components. Furthermore, other contexts, such as webservice orchestration, can be modeled as synthesis of a system from a library of components. In this work we define and study the problem of LTL synthesis from libraries of reusable components. We define two notions of composition: dataflow composition, for which we prove the problem is undecidable, and controlflow composition, for which we prove the problem is 2EXPTIMEcomplete. As a side benefit we derive an explicit characterization of the information needed by the synthesizer on the underlying components. This characterization can be used as a specification formalism between component providers and integrators.
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 ..."
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Cited by 28 (9 self)
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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
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 ..."
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Cited by 26 (6 self)
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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.
Symbolic bounded synthesis
, 2010
"... Synthesis of finite state systems from full linear time temporal logic (LTL) specifications is gaining more and more attention as several recent achievements have significantly improved its practical applicability. Many works in this area are based on the Safraless synthesis approach. Here, the com ..."
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Cited by 24 (0 self)
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Synthesis of finite state systems from full linear time temporal logic (LTL) specifications is gaining more and more attention as several recent achievements have significantly improved its practical applicability. Many works in this area are based on the Safraless synthesis approach. Here, the computation is usually performed either in an explicit way or using symbolic data structures other than binary decision diagrams (BDDs). In this paper, we close this gap and consider Safraless synthesis using BDDs as state space representation. The key to this combination is the application of novel optimisation techniques which decrease the number of state bits in such a representation significantly. We evaluate our approach on several practical benchmarks, including a new load balancing case study. Our experiments show an improvement of several orders of magnitude over previous approaches.
Pushdown Module Checking with Imperfect Information
, 2012
"... The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems ( ..."
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Cited by 23 (14 self)
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The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems (pushdown module checking). In this paper, we extend pushdown module checking to the imperfect information setting; i.e., to the case where the environment has only a partial view of the system’s control states and pushdown store content. We study the complexity of this problem with respect to the branchingtime temporal logics CTL, CTL ∗ and the propositional µcalculus. We show that pushdown module checking, which is by itself harder than pushdown model checking, becomes undecidable when the environment has imperfect information.
Debugging Formal Specifications Using Simple Counterstrategies
, 2009
"... Deriving a formal specification from an informal design intent is an errorprone process. The resulting specification may be incomplete, unrealizable, or in conflict with the design intent. We propose a debugging method for incorrect specifications that does not need an implementation. We show that ..."
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Cited by 22 (2 self)
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Deriving a formal specification from an informal design intent is an errorprone process. The resulting specification may be incomplete, unrealizable, or in conflict with the design intent. We propose a debugging method for incorrect specifications that does not need an implementation. We show that we can explain conflicts with the design intent by explaining unrealizability. Our approach for explaining unrealizability is based on counterstrategies. Since counterstrategies may be large, we propose several ways to simplify them. First, we simplify the specification itself by removing both requirements and variables that do not contribute to the problem. Second, we heuristically search for a countertrace, i.e., a single input trace that suffices to demonstrate unrealizability. Finally, we present the countertrace or the counterstrategy to the user in extensive form as a graph and implicitly as an interactive game. We present experimental results for specifications given as GR(1) formulas.