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… 

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References

SHOWING 1-10 OF 13 REFERENCES

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

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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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.