this paper we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed, (2) the number of atomic propositions, and (3) the temporal height. Key Words: logic in computer science, computational complexity, verification, temporal logic, model checking 1.

A long standing open problem in the theory of (Mazurkiewicz) traces has been the question whether LTL (Linear Time Logic) is expressively complete with respect to the rst order theory. We solve this problem positively for nite and in nite traces and for the simplest temporal logic, which is based only on next and until modalities. Similar results were established previously, but they were all weaker, since they used additional past or future modalities. Another feature of our work is that our proof is direct and does not use any reduction to the word case.

A mu-calculus over dependence graph representation of traces is considered. It is shown that the mu-calculus cannot express all monadic second order (MSO) properties of dependence graphs.

The basic modal operator bounded until of Metric Temporal Logic (MTL) comes in several variants. In particular it can be strict (when it does not constrain the current instant) or not, and matching (when it requires its two arguments to eventually hold together) or not. This paper compares the relative expressiveness of the resulting MTL variants over dense time. We prove that the expressiveness is not affected by the variations when considering non-Zeno interpretations and arbitrary nesting of temporal operators. On the contrary, the expressiveness changes for flat

A temporal logic of causality (TLC) was introduced by Alur, Penczek, and Peled in [1]. It is basically a linear time temporal logic interpreted over Mazurkiewicz traces which allows quantification over causal chains. Through this device one can directly formulate causality properties of distributed systems. In this paper we consider an extension of TLC by strengthening the chain quantification operators. We show that our logic TLC # adds to the expressive power of TLC. We do so by defining an EhrenfeuchtFra sse game to capture the expressive power of TLC. We then exhibit a property and by means of this game prove that the chosen property is not definable in TLC. We then show that the same property is definable in TLC # . We prove in fact the stronger result that TLC # is expressively stronger than TLC exactly when the dependency relation associated with the underlying trace alphabet is not transitive. We then show that TLC # defines only regular trace languages by embedding it into the...

A temporal logic of causality (TLC) was introduced by Alur, Penczek and Peled in [1]. It is basically a linear time temporal logic interpreted over Mazurkiewicz traces which allows quantification over causal chains. Through this device one can directly formulate causality properties of distributed systems. In this paper we consider an extension of TLC by strengthening the chain quantification operators. We show that our logic TLC adds to the expressive power of TLC. We do so by defining an Ehrenfeucht-Fraïssé game to capture the expressive power of TLC. We then exhibit a property and by means of this game prove that the chosen property is not definable in TLC. We then show that the same property is definable in TLC. We prove in fact the stronger result that TLC is expressively stronger than TLC exactly when the dependency relation associated with the underlying trace alphabet is not transitive.

Models ABSTRACTION + + Infinite-state On-the-Fly Verification ANALYSIS REACHABILITY SYMBOLIC FINITE-STATE ANALYSIS (T 1 ; T 2 ) Concrete Model Finite Abtract Model Abstract Model Infinite-state Finite INFINITE-STATE Invariants Figure 2: The general methodology of reachable configurations, and more generally, how to compute and represent this set effectively. One of our main research directions is: ffl Developing efficient techniques to cope with the combinatorial explosion in the size of the models, and to reduce the complexity of the state-space exploration, both in time and memory.