Julien d'Orso

Regular Tree Model Checking

In this paper, we present an approach for algorithmic verification of infinite-state systems with a parameterized tree topology. Our work is a generalization of regular model checking, where we extend the work done with strings toward trees. States are represented by trees over a finite alphabet, and transition relations by regular, structure preserving relations on trees. We use an automata theoretic method to compute the transitive closure of such a transition relation. Although the method is incomplete, we present sufficient conditions to ensure termination.We have implemented a prototype for our algorithm and show the result of its application on a number of examples.

Algorithmic Improvements in Regular Model Checking

Regular model checking is a form of symbolic model checking for parameterized and infinite-state systems, whose states can be represented as finite strings of arbitrary length over a finite alphabet, in which regular sets of words are used to represent sets of states. In earlier papers, we have developed methods for computing the transitive closure (or the set of reachable states) of the transition relation, represented by a regular length-preserving transducer. In this paper, we present several improvements of these techniques, which reduce the size of intermediate approximations of the transitive closure: One improvement is to pre-process the transducer by bi-determinization, another is to use a more powerful equivalence relation for identifying histories (columns) of states in the transitive closure. We also present a simplified theoretical framework for showing soundness of the optimization, which is based on commuting simulations. The techniques have been implemented, and we report the speedups obtained from the respective optimizations.

Regular Model Checking for LTL(MSO)

Regular model checking is a form of symbolic model checking for parameterized and infinite-state systems whose states can be represented as words of arbitrary length over a finite alphabet, in which regular sets of words are used to represent sets of states. We present LTL(MSO), a combination of the logics MSO and LTL as a natural logic for expressing temporal properties to be verified in regular model checking. LTL(MSO) is a two-dimensional modal logic, where MSO is used for specifying properties of system states and transitions, and LTL is used for specifying temporal properties. In addition, the first-order quantification in MSO can be used to express properties parameterized on a position or process. We give a technique for model checking LTL(MSO), which is adapted from the automata-theoretic approach: a formula is translated to a (Buchi) transducer with a regular set of accepting states, and regular model checking techniques are used to search for models. We have implemented the technique and show its application to a number of parameterized algorithms from the literature.

Deciding Monotonic Games.

In an earlier work [ACJYK00] we presented a general framework for verification of infinite-state transition systems, where the transition relation is monotonic with respect to a well quasi-ordering on the set of states. In this paper, we investigate extending the framework from the context of transition systems to that of games. We show that monotonic games are in general undecidable. We identify a subclass of monotonic games, called downward closed games. We provide algorithms for analyzing downward closed games subject to winning conditions which are formulated as safety properties.

Simulation-Based iteration of tree transducers

Regular model checking is the name of a family of techniques for analyzing infinite-state systems in which states are represented by words, sets of states by finite automata, and transitions by finite-state transducers. The central problem is to compute the transitive closure of a transducer. A main obstacle is that the set of reachable states is in general not regular. Recently, regular model checking has been extended to systems with tree-like architectures. In this paper, we provide a procedure, based on a new implementable acceleration technique, for computing the transitive closure of a tree transducer. The procedure consists of incrementally adding new transitions while merging states which are related according to a pre-defined equivalence relation. The equivalence is induced by a downward and an upward simulation relation which can be efficiently computed. Our technique can also be used to compute the set of reachable states without computing the transitive closure. We have implemented and applied our technique to several protocols.

Tree regular model checking: A simulation-based approach ☆

Regular model checking is the name of a family of techniques for analyzing infinite-state systems in which states are represented by words, sets of states by finite automata, and transitions by fin ...

Monotonic and Downward Closed Games

In an earlier work [Abdulla et al. (2000, Information and Computation, 160, 109–127)] we presented a general framework for verification of infinite-state transition systems, where the transition relation is monotonic with respect to a well quasi-ordering on the set of states. In this article, we investigate extending the framework from the context of transition systems to that of games with infinite state spaces. We show that monotonic games with safety winning conditions are in general undecidable. In particular, we show this negative results for games which are defined over Petri nets. We identify a subclass of monotonic games, called downward closed games. We provide algorithms for analysing downward closed games subject to safety winning conditions. We apply the algorithm to games played on lossy channel systems. Finally, we show that weak parity games are undecidable for the above classes of games.