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Unambiguous finite automaton

In automata theory, an unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path.

Version
v1 · 2026-09-28 · History
Domain-specific #
12693
Domain group
Applied Sciences & Engineering
Origin domain
Computer Science & Software Engineering
Subdomain
Automata Theory → Computer Science & Software Engineering

Core Idea

Unambiguous finite automaton is treated here as the recurring computerscienceandinformation identity summarized by this source-grounded definition: In automata theory, an unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path. In automata theory, an unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path. Each deterministic finite automaton (DFA) is an UFA, but not vice versa. DFA, UFA, and NFA recognize exactly the same class of formal languages.

Scope of Application

  • Formal definition. An NFA is represented formally by a 5-tuple, A=(Q,\Sigma,\Delta,q0,F) .

  • Formal definition. An UFA is an NFA such that, for each word w=a1a2...an , there exists at most one sequence of states r0,r1,...,rn , in Q with the following conditions.

  • Formal definition. r{i+1} \in \Delta (ri, a{i+1}) for i=0,...n-1.

  • Formal definition. In words, those conditions state that, if w is accepted by A , there is exactly one accepting path, that is, one path from an initial state to a final state that.

  • Example. Let L be the set of words over the alphabet {a,b} whose nth last letter is an a .

Clarity

A clear use of Unambiguous finite automaton names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In automata theory, an unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path.

Manages Complexity

Unambiguous finite automaton compresses multiple computerscienceandinformation details into a stable diagnostic relation. The source shows both the central mechanism—an NFA is represented formally by a 5-tuple, A=(Q,\Sigma,\Delta,q0,F) .—and the practical consequence—given a UFA A and an integer n, one can count in polynomial time the number of words of size n that are accepted by A.

Abstract Reasoning

  1. Type the carrier. Identify the computerscienceandinformation entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: In automata theory, an unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path.
  3. Check operation and conditions. In words, those conditions state that, if w is accepted by A , there is exactly one accepting path, that is, one path from an initial state to a final state that is labelled by w . 4.

Knowledge Transfer

Within the home domain. Knowledge about Unambiguous finite automaton transfers literally when a new case preserves the same carrier type, relation, and recognition test. An NFA is represented formally by a 5-tuple, A=(Q,\Sigma,\Delta,q0,F) . An UFA is an NFA such that, for each word w=a1a2...an , there exists at most one sequence of states r0,r1,...,rn , in Q with the following conditions. Beyond the home domain. No canonical parent is asserted for Unambiguous finite automaton.

Relationships to Other Abstractions

Local relationship map for Unambiguous finite automatonParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Unambiguousfinite automatonDOMAINDomain-specific abstraction: Automaton — is a kind ofAutomatonDOMAIN

Current abstraction Unambiguous finite automaton Domain-specific

Parents (1) — more general patterns this builds on

  • Unambiguous finite automaton is a kind of Automaton Domain-specific

    It is a finite automaton restricted to at most one accepting run per input.

Hierarchy paths (2) — routes to 2 parentless roots

Neighborhood in Abstraction Space

Unambiguous finite automaton sits in a crowded region of the domain-specific corpus (35th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Computation Models & Complexity Classes (37 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08