# Composed Bisimulation for Tree Automata

@article{Abdulla2009ComposedBF, title={Composed Bisimulation for Tree Automata}, author={Parosh Aziz Abdulla and Ahmed Bouajjani and Luk{\'a}{\vs} Hol{\'i}k and Lisa Kaati and Tom{\'a}{\vs} Vojnar}, journal={Int. J. Found. Comput. Sci.}, year={2009}, volume={20}, pages={685-700} }

We address the problem of reducing the size of (nondeterministic, bottom-up) tree automata using suitable, language-preserving equivalences on the states of the automata. In particular, we propose the so-called composed bisimulationas a new language preserving equivalence. Composed bisimulation is defined in terms of two different relations, namely upward and downward bisimulation. Moreover, we provide simple and efficient algorithms for computing composed bisimulation based on a reduction to…

## 17 Citations

### A Uniform (Bi-)Simulation-Based Framework for Reducing Tree Automata

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2009

### Backward and forward bisimulation minimization of tree automata

- Computer ScienceTheor. Comput. Sci.
- 2009

### Simulations and Antichains for Efficient Handling of Finite Automata

- Computer ScienceArXiv
- 2017

This thesis focuses on techniques for finite automata and their use in practice, with the main emphasis on nondeterministic tree automata, and generalises the so called antichain universality and language inclusion checking technique developed originally for finite word automata for tree Automata.

### Backward and Forward Bisimulation Minimisation of Tree Automata

- Business, Computer ScienceCIAA
- 2007

An existing bisimulation minimisation algorithm for tree automata is improved by introducing backward and forward bisimulations and developing minimisation algorithms for them, which are more effective but just as fast than the previous algorithm.

### From Tree Automata to String Automata Minimization

- Computer ScienceTheory of Computing Systems
- 2017

A reduction of the minimization problem for a bottom-up deterministic tree automaton (DFTA) is proposed, making the latter a minimization of a string deterministic finite automaton(DFA), followed by minimizing this string automaton.

### An Efficient Finite Tree Automata Library

- Computer ScienceArXiv
- 2012

Through a series of experiments it is shown that the library can compete with other available tree automata libraries, in certain areas being even significantly superior to them.

### Minimization of Symbolic Tree Automata

- Computer Science2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2016

This paper formally defines and proves the properties of minimality in the symbolic setting and presents a new algorithm based on the following idea: the problem of minimizing symbolic tree automata can be reduced to the problemof minimizing symbolic (string) automata by encoding the tree structure as part of the alphabet theory.

### Program synthesis using abstraction refinement

- Computer ScienceProc. ACM Program. Lang.
- 2018

A refinement-based synthesis algorithm that uses abstract finite tree automata (AFTA), which uses a coarse initial program abstraction to construct an initial AFTA, which is iteratively refined by constructing a proof of incorrectness of any spurious program.

### A Backward and a Forward Simulation for Weighted Tree Automata

- Computer ScienceCAI
- 2009

Two types of simulations work for wta over additively idempotent, commutative semirings and can be used to reduce the size of wta while preserving their semantics.

### Minimization of Symbolic Transducers

- Computer ScienceCAV
- 2017

The theory for and an algorithm for computing quotients of symbolic transducers under indistinguishability preserving equivalence relations over states such as bisimulation are developed and it is shown that the algorithm is a minimization algorithm in the deterministic finite state case.

## References

SHOWING 1-10 OF 13 REFERENCES

### A Uniform (Bi-)Simulation-Based Framework for Reducing Tree Automata

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2009

### Computing Simulations over Tree Automata (Efficient Techniques for Reducing Tree Automata)

- Computer Science
- 2007

It is shown that downward and upward relations can be combined to get relations compatible with the tree language equivalence, which can be used for an efficient size reduction of nondeterministic tree automata.

### Abstract regular (tree) model checking

- Computer ScienceInternational Journal on Software Tools for Technology Transfer
- 2011

This work describes how various incrementally refinable abstractions on finite (word and tree) automata can be used for verification of programs manipulating tree-like dynamic data structures and illustrates the efficiency of abstract regular (tree) model checking in verification of simple systems with various sources of infinity.

### Bisimulation Minimization of Tree Automata

- Computer ScienceInt. J. Found. Comput. Sci.
- 2007

An algorithm by Paige and Tarjan that solves the coarsest stable refinement problem to the domain of trees is extended to minimize nondeterministic tree automata (NTA) with respect to bisimulation.

### Minimization of Non-deterministic Automata with Large Alphabets

- Computer ScienceCIAA
- 2005

This paper adapts the Paige-Tarjan algorithm to the case where the labels are symbolically represented using Binary Decision Diagrams (BDDs), and shows that the algorithm has an overall complexity of ${\mathcal O}(l \cdot m \CDot log{n})$ where l is the size of the alphabet.

### A New Efficient Simulation Equivalence Algorithm

- Computer Science22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
- 2007

A new efficient simulation equivalence algorithm is presented that is obtained as a modification of Henzinger et al.'s algorithm and whose correctness is based on some techniques used in recent applications of abstract interpretation to model checking.

### Backward and Forward Bisimulation Minimisation of Tree Automata

- Business, Computer ScienceCIAA
- 2007

An existing bisimulation minimisation algorithm for tree automata is improved by introducing backward and forward bisimulations and developing minimisation algorithms for them, which are more effective but just as fast than the previous algorithm.

### Extrapolating Tree Transformations

- Computer ScienceCAV
- 2002

A general acceleration technique is presented which allows to speed up the convergence of iterative fixpoint computations in regular tree model checking and can emulate many existing algorithms for special classes of transformations and show that it can deal with transformations beyond the scope of these algorithms.

### Computing simulations on finite and infinite graphs

- Computer Science, MathematicsProceedings of IEEE 36th Annual Foundations of Computer Science
- 1995

2D rectangular automata, which model discrete reactive systems with continuous environments, define effectively presented infinite graphs with finite similarity relations and it follows that the refinement problem and the /spl forall/CTL* model-checking problem are decidable for 2D rectangular Automata.

### Three Partition Refinement Algorithms

- Computer ScienceSIAM J. Comput.
- 1987

This work presents improved partition refinement algorithms for three problems: lexicographic sorting, relational coarsest partition, and double lexical ordering that uses a new, efficient method for unmerging two sorted sets.