We prove a conjecture by A. Pnueli and strengthen it showing a sequence of "counting modalities" none of which is expressible in the temporal logic generated by the previous modalities, over the real line, or over the positive reals. Moreover, there is no finite temporal logic that can express all of them over the real line, so that no finite metric temporal logic is expressively complete.

The shuffle operator models communication free concurrency and has little expressive power (it does not produce new languages when added to regular expressions). Decidability problems for languages involving this operation were previously tackled but remained unsolved (except for a weak conjecture). We prove that language equivalence is undecidable even for a very restricted class of expressions involving the shuffle operator. This also re-proves that language equivalence is undecidable for Basic Parallel Processes.

A polynomial-time algorithm is presented for deciding bisimulation equivalence of so-called Basic Parallel Processes: multisets of elementary processes combined by a commutative parallel-composition operator.

A polynomial-time procedure is presented for deciding bisimilarity of normed context-free processes. It follows as a corollary that language equivalence of simple context-free grammars is decidable in polynomial time.>

CCS is a universal formalism: any computable function is computed by some CCS agent. Moreover, one can reduce the halting problem for Turing machines to the problem of deciding bisimilarity of two CCS agents, thus demonstrating the undecidability of the equivalence checking problem. In this paper, we demonstrate the limits of decidability of CCS. In particular, we show that by simply disallowing either of communication or both restriction and relabelling, we arrive at a sublanguage which still describes a rich class of infinite state systems but for which bisimulation is decidable. We also demonstrate complete axiomatisations for these sublanguages. We compare these results with the undecidability of all other common equivalences.

The authors prove the decidability of two subclasses of recursive processes involving a parallel composition operator with respect to bisimulation equivalence, namely, the so-called normed and live processes. To accomplish this, the authors first prove a unique decomposition result for (a generalization of) normed processes, in order to deduce a necessary cancellation law. The decidability proof leads to a complete axiomatization for these process classes.>

Using methods from model theory, the authors construct algorithms that, given any first-order predicate calculus query over a finite database, determine if they have a finite number of solutions or not, and if they do, list them all. This is done for languages that include function names (but no symbols for infinite relations) and for languages that include a name for the order of natural number or for the prefix order in a domain of strings over some alphabet (but no function symbols). The results prove some conjectures of M. Kiffer (Proc. Int. Conf. on Databases and Knowledge Bases, 1988, p.405-415).>