Sven Schewe

Uniform distributed synthesis

We provide a uniform solution to the problem of synthesizing a finite-state distributed system. An instance of the synthesis problem consists of a system architecture and a temporal specification. The architecture is given as a directed graph, where the nodes represent processes (including the environment as a special process) that communicate synchronously through shared variables attached to the edges. The same variable may occur on multiple outgoing edges of a single node, allowing for the broadcast of data. A solution to the synthesis problem is a collection of finite-state programs for the processes in the architecture, such that the joint behavior of the programs satisfies the specification in an unrestricted environment. We define information forks, a comprehensive criterion that characterizes all architectures with an undecidable synthesis problem. The criterion is effective: for a given architecture with n processes and v variables, it can be determined in O(n/sup 2//spl middot/v) time whether the synthesis problem is decidable. We give a uniform synthesis algorithm for all decidable cases. Our algorithm works for all /spl omega/-regular tree specification languages, including the /spl mu/-calculus. The undecidability proof, on the other hand, uses only LTL or, alternatively, CTL as the specification language. Our results therefore hold for the entire range of specification languages from LTL/CTL to the /spl mu/-calculus.

An Optimal Strategy Improvement Algorithm for Solving Parity and Payoff Games

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 locallyprofitable changes, and subsequently evaluate the modified strategy. This separation is unfortunate, because current strategy improvement algorithms have no effective means to predict the global effectof the individual local modifications beyond classifying them as profitable, adversarial, or stale. Furthermore, they are completely blind towards the cross effectof 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 improvementin every step, selecting the best combination of local updates from a superset of all profitable and stale changes.

Tighter Bounds for the Determinisation of Büchi Automata

The introduction of an efficient determinisation technique for Buchi automata by Safra has been a milestone in automata theory. To name only a few applications, efficient 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 satisfiability checking and model synthesis for branching- and alternating-time 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 state-space is bilinear in the size of the input alphabet and the state-space of the Rabin transition automaton, or, for large input alphabets, contains approximately (2.66 n ) n states, respectively. We also provide a flexible 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.

Synthesis of asynchronous systems

This paper addresses the problem of synthesizing an asynchronous system from a temporal specification. We show that the cost of synthesizing a single-process implementation is the same for synchronous and asynchronous systems (2EXPTIME-complete for CTL* and EXPTIME-complete for the µ-calculus) if we assume a full scheduler (i.e., a scheduler that allows every possible scheduling), and exponentially more expensive for asynchronous systems without this assumption (3EXPTIME-complete for CTL* and 2EXPTIME-complete for the µ-calculus). While multi-process synthesis for synchronous distributed systems is possible for certain architectures (like pipelines and rings), we show that the synthesis of asynchronous distributed systems is decidable if and only if at most one process implementation is unknown.

ATL* Satisfiability Is 2EXPTIME-Complete

The two central decision problems that arise during the design of safety critical systems are the satisfiability and the model checking problem. While model checking can only be applied after implementing the system, satisfiability checking answers the question whether a system that satisfies the specification exists. Model checking is traditionally considered to be the simpler problem --- for branching-time and fixed point logics such as CTL, CTL*, ATL, and the classical and alternating time μ-calculus, the complexity of satisfiability checking is considerably higher than the model checking complexity. We show that ATL* is a notable exception of this rule: Both ATL* model checking and ATL* satisfiability checking are 2EXPTIME-complete.

iscasMc: A Web-Based Probabilistic Model Checker

We introduce the web-based model checker iscasMc for probabilistic systems see http://iscasmc.ios.ac.cn/IscasMC . This Java application offers an easy-to-use web interface for the evaluation of Markov chains and decision processes against PCTL and PCTL* specifications. Compared to PRISM or MRMC, iscasMc is particularly efficient in evaluating the probabilities of LTL properties.

Satisfiability and finite model property for the alternating-time µ-calculus

This paper presents a decision procedure for the alternating-time μ-calculus. The algorithm is based on a representation of alternating-time formulas as automata over concurrent game structures. We show that language emptiness of these automata can be checked in exponential time. The complexity of our construction meets the known lower bounds for deciding the satisfiability of the classic μ-calculus. It follows that the satisfiability problem is EXPTIME-complete for the alternating-time μ-calculus.

Synthesis of distributed control through knowledge accumulation

In distributed systems, local controllers often need to impose global guarantees. A solution that will not impose additional synchronization may not be feasible due to the lack of ability of one process to know the current situation at another. On the other hand, a completely centralized solution will eliminate all concurrency. A good solution is usually a compromise between these extremes, where synchronization is allowed for in principle, but avoided whenever possible. In a quest for practicable solutions to the distributed control problem, one can constrain the executions of a system based on the pre-calculation of knowledge properties and allow for temporary interprocess synchronization in order to combine the knowledge needed to control the system. This type of control, however, may incur a heavy communication overhead. We introduce the use of simple supervisor processes that accumulate information about processes until sufficient knowledge is collected to allow for safe progression. We combine the knowledge approach with a game theoretic search that prevents progressing to states from which there is no way to guarantee the imposed constraints.

Finite optimal control for time-bounded reachability in CTMDPs and continuous-time Markov games

We establish the existence of optimal scheduling strategies for time-bounded reachability in continuous-time Markov decision processes, and of co-optimal strategies for continuous-time Markov games. Furthermore, we show that optimal control does not only exist, but has a surprisingly simple structure: the optimal schedulers from our proofs are deterministic and timed positional, and the bounded time can be divided into a finite number of intervals, in which the optimal strategies are positional. That is, we demonstrate the existence of finite optimal control. Finally, we show that these pleasant properties of Markov decision processes extend to the more general class of continuous-time Markov games, and that both early and late schedulers show this behaviour.

SMT-based synthesis of distributed systems

We apply SMT solving to synthesize distributed systems from specifications in linear-time temporal logic (LTL). The LTL formula is translated into an equivalent universal co-Büchi tree automaton. The existence of a finite transition system in the language of the automaton is then specified as a quantified formula in the theory (N,<) of the ordered natural numbers with uninterpreted function symbols. While our experimental results indicate that the resulting satisfiability problem is generally out of reach for the currently available SMT solvers, the problem immediately becomes tractable if we fix an upper bound on the number of states in the distributed system. After replacing each universal quantifier by an explicit conjunction, the SMT solver Yices solves simple single-process synthesis problems within a few seconds, and distributed synthesis problems, such as a twoprocess distributed arbiter, within one minute.