Stanislav Böhm

Equivalence of deterministic one-counter automata is NL-complete

We prove that language equivalence of deterministic one-counter automata is NL-complete. This improves the superpolynomial time complexity upper bound shown by Valiant and Paterson in 1975. Our main contribution is to prove that two deterministic one-counter automata are inequivalent if and only if they can be distinguished by a word of length polynomial in the size of the two input automata.

Bisimilarity of one-counter processes is PSPACE-complete

A one-counter automaton is a pushdown automaton over a singleton stack alphabet. We prove that the bisimilarity of processes generated by nondeterministic one-counter automata (with no e-steps) is in PSPACE. This improves the previously known decidability result (Jancar 2000), and matches the known PSPACE lower bound (Srba 2009). We add the PTIME-completeness result for deciding regularity (i.e. finiteness up to bisimilarity) of one-counter processes.

Language equivalence of deterministic real-time one-counter automata is NL-complete

We prove that deciding language equivalence of deterministic realtime one-counter automata is NL-complete, in stark contrast to the inclusion problem which is known to be undecidable. This yields a subclass of deterministic pushdown automata for which the precise complexity of the equivalence problem can be determined. Moreover, we show that deciding regularity is NL-complete as well.

Usage of petri nets for high performance computing

Petri nets are a well established graphical and mathematical modelling language for a description of concurrent systems. The main scope of this paper is to present our approach how to use Petri nets for high-performance computing. They are rarely used in this area. As a proof of concept, we are developing a tool Kaira. The modelling language in the tool is based on our extension of Coloured Petri Nets. The basic concept is to use a visual language to model parallel behaviour and communication. Sequential parts of a program are written in C/C++. In contrast to other Petri Nets based tools, Kaira is not intended only for modelling and simulation, but it can also generate standalone parallel applications from models. Generated applications use MPI and threads. This paper also presents new Kairas features including modules for computations on structured objects, more controllable semantics of mapping to MPI processes and a support for the hybrid computing.

Parallelization of ant colony optimization algorithm using Kaira

Parallel computing can be very useful for meta-heuristic algorithms, because it can reduce time to find a solution with given properties. On the other hand parallel programming is generally more difficult than the sequential one and we need more development time to get a working parallel solution. We are developing a tool named Kaira which is intended for modelling, debugging, and automated generation of parallel applications. The modelling is based on our own variant of Coloured Petri Nets. In this paper we present how to create parallel programs from an existing sequential implementation of Ant Colony Optimization Algorithm using Kaira. This approach simplifies the development process and thus saves the development time and costs.

Bisimulation equivalence and regularity for real-time one-counter automata

A one-counter automaton is a pushdown automaton with a singleton stack alphabet, where stack emptiness can be tested; it is a real-time automaton if it contains no e-transitions. We study the computational complexity of the problems of equivalence and regularity (i.e. semantic finiteness) on real-time one-counter automata. The first main result shows PSPACE -completeness of bisimulation equivalence; this closes the complexity gap between decidability 23] and PSPACE -hardness 25]. The second main result shows NL -completeness of language equivalence of deterministic real-time one-counter automata; this improves the known PSPACE upper bound (indirectly shown by Valiant and Paterson 27]). Finally we prove P -completeness of the problem if a given one-counter automaton is bisimulation equivalent to a finite system, and NL -completeness of the problem if the language accepted by a given deterministic real-time one-counter automaton is regular. Bisimulation equivalence is PSPACE -complete for real-time one-counter automata.Language equivalence is NL -complete for deterministic real-time one-counter automata.Finiteness w.r.t. bisimilarity is P -complete for real-time one-counter automata.Regularity is NL -complete for deterministic real-time one-counter automata.

Developing Parallel Applications Using Kaira

We are developing a tool named Kaira. This tool is intended for modelling, simulation and generation of parallel applications. Modelling is based on the variant of Coloured Petri Nets. Coloured Petri Nets provide the theoretical background and we use their syntax and semantics. Moreover our tool can automatically generate standalone parallel applications from the model. In this paper we present how to develop parallel applications in Kaira. Like an example we use two dimensional heat flow problem solved by Jacobi finite difference method. We present different aspects and different approaches how to model this problem in Kaira on different levels of abstraction.

State-Space Reduction of Non-deterministically Synchronizing Systems Applicable to Deadlock Detection in MPI

The paper is motivated by non-deterministic synchronizations in MPI (Message Passing Interface), where some send operations and collective operations may or may not synchronize; a correctly written MPI program should count with both options. Here we focus on the deadlock detection in such systems and propose the following reduction of the explored state space. The system is first analyzed without forcing the respective synchronizations, by applying standard partial-order reduction methods. Then a suggested algorithm is used that searches for potentially missed deadlocks caused by synchronization. In practical examples this approach leads to major reductions of the explored state-space in comparison to encoding the synchronization options into the state-space search directly. The algorithm is presented as a stand-alone abstract framework that can be also applied to the future versions of MPI as well as to other related problem domains.

Active diagnosis with observable quiescence

Active diagnosis of a discrete-event system consists in controlling the system such that faults can be detected. Here we extend the framework of active diagnosis by introducing modalities for actions and states and a new capability for the controller, namely observing that the system is quiescent. We design a game-based construction for both the decision and the synthesis problems that is computationally optimal. Furthermore we prove that the size and the delay provided by the active diagnoser (when it exists) are almost optimal.

Kaira: Development Environment for MPI Applications

This tool paper presents Kaira ( http://verif.cs.vsb.cz/kaira/ ) – a tool for simplifying development of parallel applications in the area of scientific and engineering computations for distributed memory systems. Our goal is to provide an environment in which a user can implement and experiment with his or her ideas in a short time; create a real running program; and verify its performance, scalability, and correctness. A unifying element in our approach is a visual programming language inspired by Colored Petri Nets that is used to define the parallel behavior, to show an inner state of a developed application back to the user, and for configurations of analyzes.