# On the Complexity of Bisimulation Problems for Basic Parallel Processes

@inproceedings{Mayr2000OnTC, title={On the Complexity of Bisimulation Problems for Basic Parallel Processes}, author={Richard Mayr}, booktitle={ICALP}, year={2000} }

Strong bisimilarity of Basic Parallel Processes (BPP) is decidable, but the best known algorithm has non-elementary complexity [7]. On the other hand, no lower bound for the problem was known. We show that strong bisimilarity of BPP is co-NP-hard.
Weak bisimilarity of BPP is not known to be decidable, but an NP lower bound has been shown in [31]. We improve this result by showing that weak bisimilarity of BPP is Π2p-hard.
Finally, we show that the problems if a BPP is regular (i.e…

## 19 Citations

### More on Weak Bisimilarity of Normed Basic Parallel Processes

- Computer ScienceTAMC
- 2008

A tableau method to decide weak bisimilarity of totally normed BPP is presented and from the decidability proof it is derived that a complete axiomatisation for the weak bisimulation of totallynormed B PP is derived.

### Strong Bisimilarity and Regularity of Basic Parallel Processes Is PSPACE-Hard

- Computer ScienceSTACS
- 2002

We show that the problem of checking whether two processes definable in the syntax of Basic Parallel Processes (BPP) are strongly bisimilar is PSPACE-hard.We also demonstrate that there is a…

### Complexity of weak bisimilarity and regularity for BPA and BPP

- Computer ScienceMathematical Structures in Computer Science
- 2003

It is shown how the technique for proving co-NP lower bound for weak bisimilarity of BPA can be applied to strong bisimilarities of BPP, and DP-hardness is demonstrated, which, in particular, implies both NP and co- NP- hardness.

### Strong bisimilarity of simple process algebras: complexity lower bounds

- Mathematics, Computer ScienceActa Informatica
- 2003

Abstract. We study bisimilarity and regularity problems of simple process algebras. In particular, we show PSPACE-hardness of the following problems: (i) strong bisimilarity of Basic Parallel…

### On the Complexity of Bisimulation Problems for Pushdown Automata

- Computer ScienceIFIP TCS
- 2000

It is shown that weak and strong bisimilarity of pushdown automata and finite automata is PSPACE-hard, but polynomial for every fixed finite automaton.

### Weak bisimilarity between finite-state systems and BPA or normed BPP is decidable in polynomial time

- Computer Science, MathematicsTheor. Comput. Sci.
- 2002

### Strong Bisimilarity and Regularity of Basic Process Algebra Is PSPACE-Hard

- Computer ScienceICALP
- 2002

This paper demonstrates PSPACE-hardness of strong bisimilarity and regularity checking problems of Basic Process Algebra with complexity upper bounds 2-EXPTIME.

### Undecidability of Weak Bisimilarity for PA-Processes

- MathematicsDevelopments in Language Theory
- 2002

It is proved that the problem whether two PA-processes are weakly bisimilar is undecidable, and several proof techniques are combined to provide a reduction from Post's correspondence problem to the problem.

### Results on Equivalence, Boundedness, Liveness, and Covering Problems of BPP-Petri Nets

- Mathematics, Computer SciencePetri Nets
- 2013

It is shown that the complexity of the classical boundedness problem increases from linear time to coNP-hardness, and very efficient algorithms are proposed for several variations of the boundedness and liveness problems of BPP-PNs.

### Veriication on Innnite Structures

- Computer Science
- 2000

This chapter presents a hierarchy of innnite-state systems based on the primitive operations of sequential and parallel composition, and examines the equivalence and regularity checking problems for these classes, with special emphasis on bisimulation equivalence.

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It is shown that weak and strong bisimilarity of pushdown automata and finite automata is PSPACE-hard, but polynomial for every fixed finite automaton.

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