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2. Automata theory - Wikipedia

   en.wikipedia.org/wiki/Automata_theory

   An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. 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 ...

3. Omega language - Wikipedia

   en.wikipedia.org/wiki/Omega_language

   The infinite words, or ω-words, can likewise be viewed as functions from to Σ. The set of all infinite words over Σ is denoted Σ ω. The set of all finite and infinite words over Σ is sometimes written Σ ∞ or Σ ≤ω. Thus an ω-language L over Σ is a subset of Σ ω.

4. Series (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Series_(mathematics)

   The infinite sequence of additions expressed by a series cannot be explicitly performed in sequence in a finite amount of time. However, if the terms and their finite sums belong to a set that has limits , it may be possible to assign a value to a series, called the sum of the series .

5. Subshift of finite type - Wikipedia

   en.wikipedia.org/wiki/Subshift_of_finite_type

   A renewal system is defined to be the set of all infinite concatenations of some fixed finite collection of finite words. Subshifts of finite type are identical to free (non-interacting) one-dimensional Potts models ( n -letter generalizations of Ising models ), with certain nearest-neighbor configurations excluded.

6. Generating function - Wikipedia

   en.wikipedia.org/wiki/Generating_function

   The ordinary generating function of a sequence can be expressed as a rational function (the ratio of two finite-degree polynomials) if and only if the sequence is a linear recursive sequence with constant coefficients; this generalizes the examples above. Conversely, every sequence generated by a fraction of polynomials satisfies a linear ...

7. Baire space (set theory) - Wikipedia

   en.wikipedia.org/wiki/Baire_space_(set_theory)

   The basic open sets of the product topology are cylinder sets.These can be characterized as: If any finite set of natural number coordinates I={i} is selected, and for each i a particular natural number value v i is selected, then the set of all infinite sequences of natural numbers that have value v i at position i is a basic open set.