Thread automaton
title: "Thread automaton" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["models-of-computation", "automata-(computation)"] topic_path: "general/models-of-computation" source: "https://en.wikipedia.org/wiki/Thread_automaton" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
In automata theory, the thread automaton (plural: automata) is an extended type of finite-state automata that recognizes a mildly context-sensitive language class above the tree-adjoining languages.
Formal definition
A thread automaton consists of
- a set N of states,called non-terminal symbols by Villemonte (2002), p.1r
- a set Σ of terminal symbols,
- a start state A**S ∈ N,
- a final state A**F ∈ N,
- a set U of path components,
- a partial function δ: N → U⊥, where U⊥ = U ∪ {⊥} for ⊥ ∉ U,
- a finite set Θ of transitions.
A path u1...u**n ∈ U* is a string of path components u**i ∈ U; n may be 0, with the empty path denoted by ε. A thread has the form u1...u**n:A, where u1...u**n ∈ U* is a path, and A ∈ N is a state. A thread store S is a finite set of threads, viewed as a partial function from U* to N, such that dom(S) is closed by prefix.
A thread automaton configuration is a triple , where l denotes the current position in the input string, p is the active thread, and S is a thread store containing p. The initial configuration is . The final configuration is , where n is the length of the input string and u abbreviates δ(A**S). A transition in the set Θ may have one of the following forms, and changes the current automaton configuration in the following way:
- SWAP B →a C: consumes the input symbol a, and changes the state of the active thread: : changes the configuration from to
- SWAP B →ε C: similar, but consumes no input: : changes to
- PUSH C: creates a new subthread, and suspends its parent thread: : changes to where u=δ(B) and pu∉dom(S)
- POP [B]C: ends the active thread, returning control to its parent: : changes to where δ(C)=⊥ and pu∉dom(S)
- SPUSH [C] D: resumes a suspended subthread of the active thread: : changes to where u=δ(B)
- SPOP [B] D: resumes the parent of the active thread: : changes to where δ(C)=⊥ One may prove that δ(B)=u for POP and SPOP transitions, and δ(C)=⊥ for SPUSH transitions.
An input string is accepted by the automaton if there is a sequence of transitions changing the initial into the final configuration.
Notes
References
References
- Villemonte de la Clergerie, Éric. (2002). "Proceedings of the 19th international conference on Computational linguistics -".
- Villemonte (2002), p.1r-2r
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