Jeffrey Shallit and Ming-Wei Wang. Automatic complexity of strings. Journal of Automata, Languages and Combinatorics, vol. 6 (2001), pp. 537–554. - Cristian S. Calude, Kai Salomaa and Tania K. Roblot. Finite-state complexity and randomness. Theoretical Computer Science, vol. 412 (2011), no. 41, pp. 5668–5677. - Cristian S. Calude, Kai Salomaa and Tania K. Roblot. State-size hierarchy for finite-state complexity. International Journal of Foundations of Computer Science, vol. 23 (2012), no. 1, pp. 37–50.

2012 ◽  
Vol 18 (4) ◽  
pp. 579-580
Author(s):  
Mia Minnes
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Size Hierarchy ◽  
Theoretical Computer ◽  
State Complexity ◽  
Finite State ◽  
State Size

STATE-SIZE HIERARCHY FOR FINITE-STATE COMPLEXITY

2012 ◽  
Vol 23 (01) ◽  
pp. 37-50 ◽  
Author(s):  
CRISTIAN S. CALUDE ◽  
KAI SALOMAA ◽  
TANIA K. ROBLOT
Keyword(s):  
Information Theory ◽  
The State ◽  
Turing Machines ◽  
Algorithmic Information Theory ◽  
Size Hierarchy ◽  
State Complexity ◽  
Result Show ◽  
Finite State ◽  
Algorithmic Information ◽  
State Size

Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the number of states needed for transducers used in minimal descriptions of arbitrary strings and, as our main result, show that the state-size hierarchy with respect to a standard encoding is infinite. We consider corresponding hierarchies yielded by more general computable encodings and establish that for a suitably chosen computable encoding every level of the state-size hierarchy can be strict.

scholarly journals Automata in SageMath---Combinatorics meet Theoretical Computer Science

2016 ◽  
Vol Vol. 18 no. 3 (Analysis of Algorithms) ◽  
Author(s):  
Clemens Heuberger ◽  
Daniel Krenn ◽  
Sara Kropf
Keyword(s):  
Computer Science ◽  
Finite State Machine ◽  
State Machine ◽  
Combinatorial Problems ◽  
Theoretical Computer Science ◽  
Hamming Weight ◽  
Software System ◽  
Theoretical Computer ◽  
Finite State ◽  
Mathematics Software

The new finite state machine package in the mathematics software system SageMath is presented and illustrated by many examples. Several combinatorial problems, in particular digit problems, are introduced, modeled by automata and transducers and solved using SageMath. In particular, we compute the asymptotic Hamming weight of a non-adjacent-form-like digit expansion, which was not known before.

scholarly journals Most Complex Regular Ideal Languages

2016 ◽  
Vol Vol. 18 no. 3 (Automata, Logic and Semantics) ◽  
Author(s):  
Janusz Brzozowski ◽  
Sylvie Davies ◽  
Bo Yang Victor Liu
Keyword(s):  
Computer Science ◽  
Left Ideal ◽  
Star Product ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Boolean Operations ◽  
Theoretical Computer ◽  
State Complexity ◽  
Regular Ideal ◽  
Language L

A right ideal (left ideal, two-sided ideal) is a non-empty language $L$ over an alphabet $\Sigma$ such that $L=L\Sigma^*$ ($L=\Sigma^*L$, $L=\Sigma^*L\Sigma^*$). Let $k=3$ for right ideals, 4 for left ideals and 5 for two-sided ideals. We show that there exist sequences ($L_n \mid n \ge k $) of right, left, and two-sided regular ideals, where $L_n$ has quotient complexity (state complexity) $n$, such that $L_n$ is most complex in its class under the following measures of complexity: the size of the syntactic semigroup, the quotient complexities of the left quotients of $L_n$, the number of atoms (intersections of complemented and uncomplemented left quotients), the quotient complexities of the atoms, and the quotient complexities of reversal, star, product (concatenation), and all binary boolean operations. In that sense, these ideals are "most complex" languages in their classes, or "universal witnesses" to the complexity of the various operations. Comment: 25 pages, 11 figures. To appear in Discrete Mathematics and Theoretical Computer Science. arXiv admin note: text overlap with arXiv:1311.4448

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