Symblicit algorithms for optimal strategy synthesis in monotonic Markov decision processes

When treating Markov decision processes (MDPs) with large state spaces, using explicit representations quickly becomes unfeasible. Lately, Wimmer et al. have proposed a so-called symblicit algorithm for the synthesis of optimal strategies in MDPs, in the quantitative setting of expected mean-payoff. This algorithm, based on the strategy iteration algorithm of Howard and Veinott, efficiently combines symbolic and explicit data structures, and uses binary decision diagrams as symbolic representation. The aim of this paper is to show that the new data structure of pseudo-antichains (an extension of antichains) provides another interesting alternative, especially for the class of monotonic MDPs. We design efficient pseudo-antichain based symblicit algorithms (with open source implementations) for two quantitative settings: the expected mean-payoff and the stochastic shortest path. For two practical applications coming from automated planning and LTL synthesis, we report promising experimental results w.r.t. both the run time and the memory consumption.Comment: In Proceedings SYNT 2014, arXiv:1407.493

Real-Time Synthesis is Hard!

We study the reactive synthesis problem (RS) for specifications given in Metric Interval Temporal Logic (MITL). RS is known to be undecidable in a very general setting, but on infinite words only; and only the very restrictive BRRS subcase is known to be decidable (see D'Souza et al. and Bouyer et al.). In this paper, we precise the decidability border of MITL synthesis. We show RS is undecidable on finite words too, and present a landscape of restrictions (both on the logic and on the possible controllers) that are still undecidable. On the positive side, we revisit BRRS and introduce an efficient on-the-fly algorithm to solve it

AbsSynthe: abstract synthesis from succinct safety specifications

In this paper, we describe a synthesis algorithm for safety specifications described as circuits. Our algorithm is based on fixpoint computations, abstraction and refinement, it uses binary decision diagrams as symbolic data structure. We evaluate our tool on the benchmarks provided by the organizers of the synthesis competition organized within the SYNT'14 workshop.Comment: In Proceedings SYNT 2014, arXiv:1407.493

On the verification of parametric and real-time systems

2009 - 2010Parametric and Real-Time Systems play a central role in the theory underlying the Verification and Synthesis problems. Real-time systems are present everywhere and are used in safety critical applications, such as flight controllers. Failures in such systems can be very expensive and even life threatening and, moreover, they are quite hard to design and verify. For these reasons, the development of formal methods for the modeling and analysis of safety-critical systems is an active area of computer science research. The standard formalism used to specify the wished behaviour of a realtime system is temporal logic. Traditional temporal logics, such as linear temporal logic (LTL), allow only qualitative assertions about the temporal ordering of events. However, in several circumstances, for assessing the efficiency of the system being modeled, it may be useful to have additional quantitative guarantees. An extension of LTL with a real-time semantics is given by the Metric Interval Temporal Logic (MITL), where changes of truth values happen according to a splitting of the line of non-negative reals into intervals. However, even with quantitative temporal logics, we would actually like to find out what quantitative bounds can be placed on the logic operators. In this thesis we face with the above problem proposing a parametric extension of MITL, that is the parametric metric interval temporal logic (PMITL), which allows to introduce parameters within intervals . For this logic, we study decision problems which are the analogous of satisfiability, validity and model-checking problems for non-parametric temporal logic. PMITL turns out to be decidable and we show that, when parameter valuations give only non-singular sets, the considered problems are all decidable, EXPSPACE-complete, and have the same complexity as in MITL. Moreover, we investigate the computational complexity of these problems for natural fragments of PMITL, and show that in meaningful fragments of the logic they are PSPACE-complete. We also consider a remarkable problem expressed by queries where the values that each parameter may assume are either existentially or universally quantified. We solve this problem in several cases and we propose an algorithm in EXPSPACE. Another interesting application of the temporal logic is when it is used to express specification of concurrent programs, where programs and properties are formalized as regular languages of infinite words. In this case, the verification problem (whether the program satisfies the specification) corresponds to solve the language inclusion problem. In the second part of this thesis we consider the Synthesis problem for realtime systems, investigating the applicability of automata constructions that avoid determinization for solving the language inclusion problem and the realizability problem for real-time logics. Since Safra’s determinization procedure is difficult to implement, we present Safraless algorithms for automata on infinite timed words. [edited by author]IX n.s

Regular Methods for Operator Precedence Languages

The operator precedence languages (OPLs) represent the largest known subclass of the context-free languages which enjoys all desirable closure and decidability properties. This includes the decidability of language inclusion, which is the ultimate verification problem. Operator precedence grammars, automata, and logics have been investigated and used, for example, to verify programs with arithmetic expressions and exceptions (both of which are deterministic pushdown but lie outside the scope of the visibly pushdown languages). In this paper, we complete the picture and give, for the first time, an algebraic characterization of the class of OPLs in the form of a syntactic congruence that has finitely many equivalence classes exactly for the operator precedence languages. This is a generalization of the celebrated Myhill-Nerode theorem for the regular languages to OPLs. As one of the consequences, we show that universality and language inclusion for nondeterministic operator precedence automata can be solved by an antichain algorithm. Antichain algorithms avoid determinization and complementation through an explicit subset construction, by leveraging a quasi-order on words, which allows the pruning of the search space for counterexample words without sacrificing completeness. Antichain algorithms can be implemented symbolically, and these implementations are today the best-performing algorithms in practice for the inclusion of finite automata. We give a generic construction of the quasi-order needed for antichain algorithms from a finite syntactic congruence. This yields the first antichain algorithm for OPLs, an algorithm that solves the ExpTime-hard language inclusion problem for OPLs in exponential time