### Abstract

This work presents a machine-checked tree automata library for Standard-ML, OCaml and Haskell. The algorithms are efficient by using appropriate data structures like RB-trees. The available algorithms for non-deterministic automata include membership query, reduction, intersection, union, and emptiness check with computation of a witness for non-emptiness. The executable algorithms are derived from less-concrete, non-executable algorithms using data-refinement techniques. The concrete data structures are from the Isabelle Collections Framework. Moreover, this work contains a formalization of the class of tree-regular languages and its closure properties under set operations.

### License

BSD License

### Topics

- Computer science/Automata and formal languages

### Session Tree-Automata

- Tree
- Ta
- AbsAlgo
- Ta_impl
- Ta_impl_codegen

### Depends on

- Collections Framework

### Auto-related entries

- Gale-Shapley Algorithm
- Regular Tree Relations
- Büchi Complementation
- IP Addresses
- A Separation Logic Framework for Imperative HOL

## Cite

×

Tree-Automata-AFP

    @article{Tree-Automata-AFP,
      author  = {Peter Lammich},
      title   = {Tree Automata},
      journal = {Archive of Formal Proofs},
      month   = {November},
      year    = {2009},
      note    = {\url{https://isa-afp.org/entries/Tree-Automata.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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