Decidability of Weak Simulation on One-Counter Nets

One-counter nets (OCN) are Petri nets with exactly one unbounded place. They are equiv-alent to a subclass of one-counter automata with only a weak test for zero. We show that weak simulation preorder is decidable for OCN and that weak simulation approximants do not converge at level ω, but only at ω2. In contrast, other semantic relations like weak bisimulation are undecidable for OCN [17], and so are weak (and strong) trace inclusion (Sec. 7).

Beyond Language Equivalence on Visibly Pushdown Automata

We study (bi)simulation-like preorder/equivalence checking on the class of visibly pushdown automata and its natural subclasses visibly BPA (Basic Process Algebra) and visibly one-counter automata. We describe generic methods for proving complexity upper and lower bounds for a number of studied preorders and equivalences like simulation, completed simulation, ready simulation, 2-nested simulation preorders/equivalences and bisimulation equivalence. Our main results are that all the mentioned equivalences and preorders are EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for visibly one-counter automata improves also the previously known DP-hardness results for ordinary one-counter automata and one-counter nets. Finally, we study regularity checking problems for visibly pushdown automata and show that they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC

Properties of Distributed Time Arc Petri Nets

In recent work we started a research on a distributed-timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required for enabling. This formalism enables to model e.g. hardware architectures like GALS. We give a formal definition of process semantics for our model and investigate several properties of local versus global timing: expressiveness, reachability and coverability

Adaptable processes

We propose the concept of adaptable processes as a way of overcoming the limitations that process calculi have for describing patterns of dynamic process evolution. Such patterns rely on direct ways of controlling the behavior and location of running processes, and so they are at the heart of the adaptation capabilities present in many modern concurrent systems. Adaptable processes have a location and are sensible to actions of dynamic update at runtime; this allows to express a wide range of evolvability patterns for concurrent processes. We introduce a core calculus of adaptable processes and propose two verification problems for them: bounded and eventual adaptation. While the former ensures that the number of consecutive erroneous states that can be traversed during a computation is bound by some given number k, the latter ensures that if the system enters into a state with errors then a state without errors will be eventually reached. We study the (un)decidability of these two problems in several variants of the calculus, which result from considering dynamic and static topologies of adaptable processes as well as different evolvability patterns. Rather than a specification language, our calculus intends to be a basis for investigating the fundamental properties of evolvable processes and for developing richer languages with evolvability capabilities

Equivalence of infinite-state systems with silent steps

This dissertation contributes to analysis methods for infinite-state systems. The dissertation focuses on equivalence testing for two relevant classes of infinite-state systems: commutative context-free processes, and one-counter automata. As for equivalence notions, we investigate the classical bisimulation and simulation equivalences. The important point is that we allow for silent steps in the model, abstracting away from internal, unobservable actions. Very few decidability results have been known so far for bisimulation or simulation equivalence for infinite-state systems with silent steps, as presence of silent steps makes the equivalence problem arguably harder to solve. A standard technique for bisimulation or simulation equivalence testing is to use the hierarchy of approximants. For an effective decision procedure the hierarchy must stabilize (converge) at level omega, the first limit ordinal, which is not the case for the models investigated in this thesis. However, according to a long-standing conjecture, the community believed that the convergence actually takes place at level omega+ omega in the class of commutative context free processes. We disprove the conjecture and provide a lower bound of omega * omega for the convergence level. We also show that all previously known positive decidability results for BPPs can be re-proven uniformly using the improved approximants techniques. Moreover dissertation contains an unsuccesfull attack on one of the main open problems in the area: decidability of weak bisimulation equivalence for commutative context-free processes. Our technical development of this section is not sufficient to solve the problem, but we believe it is a serious step towards a solution. Furtermore, we are able to show decidability of branching (stuttering) bisimulation equivalence, a slightly more discriminating variant of bisimulation equivalence. It is worth emphesizing that, until today, our result is the only known decidability result for bisimulation equivalence in a class of inifinite-state systems with silent steps that is not known to admit convergence of (some variant of) standard approximants at level omega. Finally we consider weak simulation equivalence over one-counter automata without zero tests (allowing zero tests implies undecidability). While weak bisimulation equivalence is known to be undecidable in this class, we prove a surprising result that weak simulation equivalence is actually decidable. Thus we provide a first example going against a trend, widely-believed by the community, that simulation equivalence tends to be computationally harder than bisimulation equivalence. In short words, the dissertation contains three new results, each of them solving a non-trivial open problem about equivalence testing of infinite-state systems with silent steps