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

@article{Hirshfeld1994APA, title={A Polynomial Algorithm for Deciding Bisimilarity of Normed Context-Free Processes}, author={Yoram Hirshfeld and Mark Jerrum and Faron Moller}, journal={Theor. Comput. Sci.}, year={1994}, volume={158}, pages={143-159} }

## 146 Citations

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

- Computer ScienceCONCUR
- 1994

A deterministic algorithm which runs in time O(n 4 v) where v is the norm of the processes being compared, which corresponds to the shortest distance to a terminating state of the process, or the shortest word generated by the corresponding grammar.

### Faster Algorithm for Bisimulation Equivalence of Normed Context-Free Processes

- Computer ScienceMFCS
- 2006

An alternative algorithm working in O(n^8 {\sl polylog} n) time is given and the best known upper bound for testing equivalence of simple context-free grammars is improved.

### Complexity of deciding bisimilarity between normed BPA and normed BPP

- Computer Science, MathematicsInf. Comput.
- 2010

### 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.

### A Polynomial Time Algorithm for Deciding Branching Bisimilarity on Totally Normed BPA

- Computer ScienceArXiv
- 2014

To the knowledge, this is the first bisimilarity checking algorithm on infinite state systems which runs in polynomial time and the correctness of the algorithm cannot be directly generalized from previous works, but the correctness proof turns out to be subtle.

### Partially-Commutative Context-Free Processes

- Computer Science, MathematicsCONCUR
- 2009

This work provides one polynomial-time algorithm that works in a superclass of both normed BPA and BPP, a new process class introduced in the paper and seems to be of independent interest.

### Bisimilarity on Basic Process Algebra is in 2-ExpTime (an explicit proof)

- MathematicsLog. Methods Comput. Sci.
- 2012

A self-contained direct proof of the membership in 2-ExpTime is given via a Prover-Refuter game which shows that there is an alternating Turing machine deciding the problem in exponential space.

### Partially-commutative context-free processes: Expressibility and tractability

- Computer Science, MathematicsInf. Comput.
- 2011

### Normed BPA vs. Normed BPP Revisited

- Computer ScienceCONCUR
- 2008

We present a polynomial-time algorithm deciding bisimilarity between a normed BPA process and a normed BPP process. This improves the previously known exponential upper bound by Cerna, KÅ™etinskĆ½,ā€¦

### Branching Bisimilarity between Finite-State Systems and BPA or Normed BPP Is Polynomial-Time Decidable

- Computer Science, MathematicsAPLAS
- 2009

The algorithm for BPA improves a previous one given by Ku***era and Mayr, while the one for normed BPP demonstrates the polynomial-time decidability of the problem, which was unknown previously.

## References

SHOWING 1-10 OF 27 REFERENCES

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

- Computer ScienceCONCUR
- 1994

A deterministic algorithm which runs in time O(n 4 v) where v is the norm of the processes being compared, which corresponds to the shortest distance to a terminating state of the process, or the shortest word generated by the corresponding grammar.

### Undecidable Equivalences for Basic Process Algebra

- Computer ScienceInf. Comput.
- 1994

All other equivalences in the linear/branching time hierarchy are examined and it is shown that none of them are decidable for normed BPA processes.

### Bisimulation Equivalence is Decidable for All Context-Free Processes

- Computer ScienceInf. Comput.
- 1992

It is shown that bisimulation equivalence is decidable for BPA and this result would be a proper extension of Milner's axiom system for regular processes for normed BPA processes.

### Decidability of bisimulation equivalence for process generating context-free languages

- Computer ScienceJACM
- 1993

A short proof of the solvability of the equivalence problem for simple context-free languages is given and a model of process graphs modulo bisimulation equivalence is given.

### Decidability of Bisimulation Equivalence for Processes Generating Context-Free Languages

- Computer SciencePARLE
- 1987

A short proof of the solvability of the equivalence problem for simple context-free languages is given and a model of process graphs modulo bisimulation equivalence is given.

### Deciding Bisimilarity of Normed Context-Free Processes is in Sigma^p_2

- Computer ScienceTheor. Comput. Sci.
- 1994

### A Short Proof of the Decidability of Bisimulation for Normed BPA-Processes

- MathematicsInf. Process. Lett.
- 1992

### Actions speak louder than words: proving bisimilarity for context-free processes

- Computer Science[1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science
- 1991

A much simpler and much more direct proof of this result is provided now, using a tableau decision method involving goal-directed rules and providing the essential part of the bisimulation relation between two processes which underlies their equivalence.

### 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-compositionā€¦

### Decidability Questions for Bismilarity of Petri Nets and Some Related Problems

- Computer ScienceSTACS
- 1994

The main result is undecidability of bisimilarity for labelled (place / transition) Petri nets. The same technique applies to the (prefix) language equivalence and reachability set equality, whichā€¦