# 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…

## 20 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…

### 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.

### Complexity Results for Problems of Communication-Free Petri Nets and Related Formalisms

- Mathematics, Computer ScienceFundam. Informaticae
- 2015

This work investigates several computational problems of communication-free Petri nets, and develops very efficient mostly linear time algorithms for different variations of the boundedness and liveness problems of cf-PNs, and uses known results for such grammars to give a coNEXPTIME-upper bound for the equivalence problem of cf -PNs.

## References

SHOWING 1-10 OF 39 REFERENCES

### Weak Bisimulation and Model Checking for Basic Parallel Processes

- Computer ScienceFSTTCS
- 1996

It is shown that unlike for general Petri nets, it is decidable if a BPP and a finite-state system are weakly bisimilar, which is the first decidability result for weak bisimulation and a non-trivial class of infinite-state systems.

### Undecidability of Bisimilarity for Petri Nets and Some Related Problems

- Computer ScienceTheor. Comput. Sci.
- 1995

### Bisimulation Equivalence is Decidable for Basic Parallel Processes

- Computer Science, MathematicsCONCUR
- 1993

The decidability proof permits the authors to present a complete axiomatisation for this class of basic parallel processes, which can be viewed as a proper extension of Milner's complete axomatisation of bisimulation equivalence on regular processes.

### A Polynomial Algorithm for Deciding Bisimilarity of Normed Context-Free Processes

- Computer ScienceTheor. Comput. Sci.
- 1996

### Regularity is Decidable for Normed BPA and Normed BPP Processes in Polynomial Time

- Mathematics, Computer ScienceSOFSEM
- 1996

A rich subclass of normed PA processes is obtained (called sPA) where the regularity is also decidable in polynomial time and constructiveness of this result implies decidability of bisimilarity for pairs of processes such that one process of this pair is sPA and the other has finitely many states.

### Weak Bisimilarity with Infinite-State Systems Can Be Decided in Polynomial Time

- Computer Science, MathematicsCONCUR
- 1999

We prove that weak bisimilarity is decidable in polynomial time between BPA and finite-state processes, and between normed BPP and finite-state processes.To the best of our knowledge, these are the…

### An Elementary Bisimulation Decision Procedure for Arbitrary Context-Free Processes

- Computer ScienceMFCS
- 1995

The point of the algorithm is the effective construction of a finite relation characterizing all bisimulation equivalence classes, whose mere existence was exploited for the decidability result.

### Deciding Finiteness of Petri Nets Up To Bisimulation

- Computer ScienceICALP
- 1996

We study the following problems for strong and weak bisimulation equivalence: given a labelled Petri net and a finite transition system, are they equivalent?; given a labelled Petri net, is it…