# Approximating Weak Bisimilarity of Basic Parallel Processes

@inproceedings{Hofman2012ApproximatingWB, title={Approximating Weak Bisimilarity of Basic Parallel Processes}, author={Piotr Hofman and Patrick Totzke}, booktitle={Combined International Workshop Expressiveness Concurrency and Workshop Structural Operational Semantics}, year={2012} }

This paper explores the well known approximation approach to decide weak bisimilarity of Basic Parallel Processes. We look into how different refinement functions can be used t o prove weak bisimilarity decidable for certain subclasses. We also show their limitations for the general case. In particular, we show a lower bound of ω ∗ ω for the approximants which allow weak steps and a lower bound of ω+ ω for the approximants that allow sequences of actions. The former lower bound negatively…

## 5 Citations

### Decidability of bisimulation on normed commutative context-free processes with silent moves

- Mathematics
- 2013

We investigate normed commutative context-free processes (Basic Parallel Processes). We show that branching bisimilarity admits the bounded response property : in the Bisimulation Game, Duplicator…

### Equivalence of infinite-state systems with silent steps

- Mathematics
- 2014

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…

### Decidability of Branching Bisimulation on Normed Commutative Context-Free Processes

- MathematicsTheory of Computing Systems
- 2013

It is shown that branching bisimilarity admits the bounded response property: in the Bisimulation Game, Duplicator always has a response leading to a process of size linearly bounded with respect to the Spoiler’s process.

## References

SHOWING 1-10 OF 19 REFERENCES

### Weak Bisimulation Approximants

- Computer Science, MathematicsCSL
- 2006

This paper investigates for this class of processes the minimal ordinal α such that ≈ = ≈α, and reduces a long-standing bound on the approximation hierarchy for weak bisimilarity ≈ over BPP, and shows that ${\approx} = {\approx_{\omega^ \omega}}$.

### 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…

### Decidability of Weak Bisimilarity for a Subset of Basic Parallel Processes

- Computer ScienceFoSSaCS
- 2001

For full Petri nets Jancar proved that bisimulation equivalence is undecidable, and decidability of bisimilarity was also shown for Basic Parallel processes, a restricted subset of Petrinets.

### 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.

### Strong bisimilarity on basic parallel processes in PSPACE-complete

- Computer Science18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.
- 2003

The paper shows an algorithm which, given a basic parallel processes (BPP) system, constructs a set of linear mappings which characterize the (strong) bisimulation equivalence on the system, and shows that PSPACE-completeness is established.

### Decidability and complexity of equivalences for simple process algebras

- Mathematics
- 1999

In this thesis I study decidability, complexity and structural properties of strong and weak bisimilarity with respect to two process algebras, Basic Process Algebras and Basic Parallel Process…

### The Joys of Bisimulation

- Computer ScienceMFCS
- 1998

This paper reviews results about bisimulation, from bothh the point of view of automata and from a logical points of view, and offers a new undefinability result.

### Petri Nets and the Equivalence Problem

- Mathematics
- 1993

We prove that trace equivalence is undecidable for the very small and natural subclass of Petri nets in which no transition requires more than one token; this subclass corresponds exactly to the…

### A polynomial-time algorithm for deciding bisimulation equivalence of normed Basic Parallel Processes

- Computer ScienceMathematical Structures in Computer Science
- 1996

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…