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  2. Alphabet (formal languages) - Wikipedia

    en.wikipedia.org/wiki/Alphabet_(formal_languages)

    For example, the alphabet of lowercase letters "a" through "z" can be used to form English words like "iceberg" while the alphabet of both upper and lower case letters can also be used to form proper names like "Wikipedia". A common alphabet is {0,1}, the binary alphabet, and a "00101111" is an example of a binary string.

  3. Deterministic finite automaton - Wikipedia

    en.wikipedia.org/wiki/Deterministic_finite_automaton

    The figure illustrates a deterministic finite automaton using a state diagram. In this example automaton, there are three states: S 0, S 1, and S 2 (denoted graphically by circles). The automaton takes a finite sequence of 0s and 1s as input. For each state, there is a transition arrow leading out to a next state for both 0 and 1.

  4. Automata theory - Wikipedia

    en.wikipedia.org/wiki/Automata_theory

    An automaton with a finite number of states is called a finite automaton (FA) or finite-state machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type of automaton. This automaton consists of states (represented in the figure by circles) and transitions (represented by arrows).

  5. Unambiguous finite automaton - Wikipedia

    en.wikipedia.org/wiki/Unambiguous_finite_automaton

    Let be the set of words over the alphabet {a,b} whose nth last letter is an . The figures show a DFA and a UFA accepting this language for n=2. Deterministic automaton (DFA) for the language L for n=2 Unambiguous finite automaton (UFA) for the language L for n=2

  6. Combinatorics on words - Wikipedia

    en.wikipedia.org/wiki/Combinatorics_on_words

    With finite automata, the edges are labeled with a letter in an alphabet. To use the graph, one starts at a node and travels along the edges to reach a final node. The path taken along the graph forms the word. It is a finite graph because there are a countable number of nodes and edges, and only one path connects two distinct nodes. [1]

  7. Separating words problem - Wikipedia

    en.wikipedia.org/wiki/Separating_words_problem

    For proving bounds on this problem, it may be assumed without loss of generality that the inputs are strings over a two-letter alphabet. For, if two strings over a larger alphabet differ then there exists a string homomorphism that maps them to binary strings of the same length that also differ. Any automaton that distinguishes the binary ...

  8. Quantum finite automaton - Wikipedia

    en.wikipedia.org/wiki/Quantum_finite_automaton

    The automata work by receiving a finite-length string = (,,,) of letters from a finite alphabet, and assigning to each such string a probability ⁡ indicating the probability of the automaton being in an accept state; that is, indicating whether the automaton accepted or rejected the string.

  9. Büchi automaton - Wikipedia

    en.wikipedia.org/wiki/Büchi_automaton

    Formally, a deterministic Büchi automaton is a tuple A = (Q,Σ,δ,q 0,F) that consists of the following components: Q is a finite set. The elements of Q are called the states of A. Σ is a finite set called the alphabet of A. δ: Q × Σ → Q is a function, called the transition function of A. q 0 is an element of Q, called the initial state ...