In this paper, we define a new class of combined automata, called temporalized automata, which can be viewed as the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Furthermore, we successfully apply temporalized automata to provide the full secondorder theory of k-refinable downward unbounded layered structures with a temporal logic counterpart. Finally, we show how temporalized automata can be used to deal with relevant classes of reactive systems, such as granular reactive systems and mobile reactive systems.

The present Thesis addresses the problem of specification and verification of communicating systems with value passing. We assume that such systems are described in the well-known Calculus of Communicating Systems, or rather, in its value passing version. As a specification language we propose an extension of the Modal ¯-Calculus, a poly-modal first-order logic with recursion. For this logic we develop a proof system for verifying judgements of the form b ` E : \Phi where E is a sequential CCS term and b is a Boolean assumption about the value variables occurring free in E and \Phi. Proofs conducted in this proof system follow the structure of the process term and the formula. This syntactic approach makes proofs easier to comprehend and machine assist. To avoid the introduction of global proof rules we adopt a technique of tagging fixpoint formulae with all relevant information needed for the discharge of reoccurring sequents. We provide such tagged formulae with a suitable semantics...

One source of complexity in the µ-calculus is its ability to specify an unbounded number of switches between universal (AX) and existential (EX) branching modes. We therefore study the problems of satis ability, validity, model checking, and implication for the universal and existential fragments of the µ-calculus, in which only one branching mode is allowed. The universal fragment is rich enough to express most specifications of interest, and therefore improved algorithms are of practical importance. We show that while the satis ability and validity problems become indeed simpler for the existential and universal fragments, this is, unfortunately, not the case for model checking and implication.

We present a model-checking algorithm for fragment L 2 of the propositional modal - calculus [12, 7] based on distributive functions. We illustrate the usefulness of our approach by uniformly deriving fast L 2 -model-checking algorithms both for finite transition systems as well as for infinite-state transition systems like pushdown processes. 1 Introduction The propositional modal -calculus as considered by Kozen in [12] has been proven to be extremely useful for the verification of finite state systems. Although not being very intuitive for expressing system properties, - calculus has been successfully used as an intermediate formalism for many temporal logics to be compiled into. While the best known algorithms for checking arbitrary closed -formulas on finite transition systems are still exponential in the alternation-depth of the formula [8, 13, 19], it has been observed that, luckily, standard translations of temporal logics like CTL , PDL\Gamma\Delta and ECTL do not result i...

Notation and Abbreviations 3 1