Abstract. We develop an automata-theoretic framework for reasoning about infinitestate sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by an alternating two-way tree automaton that navigates through the tree. As has been the case with finite-state systems, the automatatheoretic framework is quite versatile. We demonstrate it by solving several versions of the model-checking problem for §-calculus specifications and prefixrecognizable systems, and by solving the realizability and synthesis problems for §-calculus specifications with respect to prefix-recognizable environments. 1

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Abstract. Metric Temporal Logic (MTL) is a prominent specification formalism for realtime systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also consider the model-checking problem for MTL: whether all words accepted by a given Alur-Dill timed automaton satisfy a given MTL formula. We show that this problem is decidable over finite words. Over infinite words, we show that model checking the safety fragment of MTL— which includes invariance and time-bounded response properties—is also decidable. These results are quite surprising in that they contradict various claims to the contrary that have appeared in the literature. 1.

Timed computation tree logic (Tctl) extends Ctl by allowing timing constraints on the temporal operators. The semantics of Tctl is defined on a dense tree. The satisfiability of Tctl-formulae is undecidable even if the structures are restricted to dense trees obtained from timed graphs. According to the known results there are two possible causes of such undecidability: the denseness of the underlying structure and the equality in the timing constraints. We prove that the second one is the only source of undecidability when the structures are defined by timed graphs. In fact, if the equality is not allowed in the timing constraints of Tctl-formulae then the finite satisfiability in Tctl is decidable. We show this result by reducing this problem to the emptiness problem of timed tree automata, so strengthening the already well-founded connections between finite automata and temporal logics. 1 Introduction In 1977 Pnueli proposed Temporal Logic as a formalism to specify and ve...

We define the class of micro-macro stack graphs, a new class of graphs modeling infinite-state sequential systems with a decidable model-checking problem. Micro-macro stack graphs are the configuration graphs of stack automata whose states are partitioned into micro and macro states. Nodes of the graph are configurations of the stack automaton where the state is a macro state. Edges of the graph correspond to the sequence of micro steps that the automaton makes between macro states. We prove that this class strictly contains the class of prefix-recognizable graphs. We give a direct automata-theoretic algorithm for model checking ¢-calculus formulas over micro-macro stack graphs. 1

Algorithmic verification is one of the most successful applications of automated reasoning in computer science. In algorithmic verification one uses algorithmic techniques to establish the correctness of the system under verification with respect to a given property. Model checking is an algorithmic-verification technique that is based on a small number of key ideas, tying together graph theory, automata theory, and logic. In this self-contained talk I will describe how this "holy trinity" gave rise to algorithmic-verification tools, and discuss its applicability to database verification.