Timed pushdown automata revisited

This paper contains two results on timed extensions of pushdown automata (PDA). As our first result we prove that the model of dense-timed PDA of Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with timeless stack. Motivated by this result, we advocate the framework of first-order definable PDA, a specialization of PDA in sets with atoms, as the right setting to define and investigate timed extensions of PDA. The general model obtained in this way is Turing complete. As our second result we prove NEXPTIME upper complexity bound for the non-emptiness problem for an expressive subclass. As a byproduct, we obtain a tight EXPTIME complexity bound for a more restrictive subclass of PDA with timeless stack, thus subsuming the complexity bound known for dense-timed PDA.Comment: full technical report of LICS'15 pape

Saturation-Based Model Checking of Higher-Order Recursion Schemes

Model checking of higher-order recursion schemes (HORS) has recently been studied extensively and applied to higher-order program verification. Despite recent efforts, obtaining a scalable model checker for HORS remains a big challenge. We propose a new model checking algorithm for HORS, which combines two previous, independent approaches to higher-order model checking. Like previous type-based algorithms for HORS, it directly analyzes HORS and outputs intersection types as a certificate, but like Broadbent et al.\u27s saturation algorithm for collapsible pushdown systems (CPDS), it propagates information backward, in the sense that it starts with target configurations and iteratively computes their pre-images. We have implemented the new algorithm and confirmed that the prototype often outperforms TRECS and CSHORe, the state-of-the-art model checkers for HORS

Module checking of pushdown multi-agent systems

In this paper, we investigate the module-checking problem of pushdown multi-agent systems (PMS) against ATL and ATL* specifications. We establish that for ATL, module checking of PMS is 2EXPTIME-complete, which is the same complexity as pushdown module-checking for CTL. On the other hand, we show that ATL* module-checking of PMS turns out to be 4EXPTIME-complete, hence exponentially harder than both CTL* pushdown module-checking and ATL* model-checking of PMS. Our result for ATL* provides a rare example of a natural decision problem that is elementary yet but with a complexity that is higher than triply exponential-time.Comment: arXiv admin note: substantial text overlap with arXiv:1709.0210

Pushdown Processes: Games and Model Checking

Games given by transition graphs of pushdown processes are considered.It is shown that if there is a winning strategy in such agame then there is a winning strategy that is realized by a pushdownprocess. This fact turns out to be connected with the model checkingproblem for the pushdown automata and the propositional mu-calculus.It is shown that this model checking problem is DEXPTIME-complete

Reasoning about LTL Synthesis over finite and infinite games

In the last few years, research formal methods for the analysis and the verification of properties of systems has increased greatly. A meaningful contribution in this area has been given by algorithmic methods developed in the context of synthesis. The basic idea is simple and appealing: instead of developing a system and verifying that it satisfies its specification, we look for an automated procedure that, given the specification returns a system that is correct by construction. Synthesis of reactive systems is one of the most popular variants of this problem, in which we want to synthesize a system characterized by an ongoing interaction with the environment. In this setting, large effort has been devoted to analyze specifications given as formulas of linear temporal logic, i.e., LTL synthesis. Traditional approaches to LTL synthesis rely on transforming the LTL specification into parity deterministic automata, and then to parity games, for which a so-called winning region is computed. Computing such an automaton is, in the worst-case, double-exponential in the size of the LTL formula, and this becomes a computational bottleneck in using the synthesis process in practice. The first part of this thesis is devoted to improve the solution of parity games as they are used in solving LTL synthesis, trying to give efficient techniques, in terms of running time and space consumption, for solving parity games. We start with the study and the implementation of an automata-theoretic technique to solve parity games. More precisely, we consider an algorithm introduced by Kupferman and Vardi that solves a parity game by solving the emptiness problem of a corresponding alternating parity automaton. Our empirical evaluation demonstrates that this algorithm outperforms other algorithms when the game has a small number of priorities relative to the size of the game. In many concrete applications, we do indeed end up with parity games where the number of priorities is relatively small. This makes the new algorithm quite useful in practice. We then provide a broad investigation of the symbolic approach for solving parity games. Specifically, we implement in a fresh tool, called SPGSolver, four symbolic algorithms to solve parity games and compare their performances to the corresponding explicit versions for different classes of games. By means of benchmarks, we show that for random games, even for constrained random games, explicit algorithms actually perform better than symbolic algorithms. The situation changes, however, for structured games, where symbolic algorithms seem to have the advantage. This suggests that when evaluating algorithms for parity-game solving, it would be useful to have real benchmarks and not only random benchmarks, as the common practice has been. LTL synthesis has been largely investigated also in artificial intelligence, and specifically in automated planning. Indeed, LTL synthesis corresponds to fully observable nondeterministic planning in which the domain is given compactly and the goal is an LTL formula, that in turn is related to two-player games with LTL goals. Finding a strategy for these games means to synthesize a plan for the planning problem. The last part of this thesis is then dedicated to investigate LTL synthesis under this different view. In particular, we study a generalized form of planning under partial observability, in which we have multiple, possibly infinitely many, planning domains with the same actions and observations, and goals expressed over observations, which are possibly temporally extended. By building on work on two-player games with imperfect information in the Formal Methods literature, we devise a general technique, generalizing the belief-state construction, to remove partial observability. This reduces the planning problem to a game of perfect information with a tight correspondence between plans and strategies. Then we instantiate the technique and solve some generalized planning problems