Describing Periodicity in Two-Way Deterministic Finite Automata Using Transformation Semigroups

2011 ◽  
pp. 324-336 ◽  
Author(s):  
Michal Kunc ◽  
Alexander Okhotin
Keyword(s):  
Finite Automata ◽  
Transformation Semigroups ◽  
Deterministic Finite Automata

Deterministic finite automata with recursive calls and DPDAs

2003 ◽  
Vol 87 (4) ◽  
pp. 187-193
Author(s):  
Jean H. Gallier ◽  
Salvatore La Torre ◽  
Supratik Mukhopadhyay
Keyword(s):  
Finite Automata ◽  
Deterministic Finite Automata

The detection and stabilisation of limit cycle for deterministic finite automata

2017 ◽  
Vol 91 (4) ◽  
pp. 874-886 ◽  
Author(s):  
Xiaoguang Han ◽  
Zengqiang Chen ◽  
Zhongxin Liu ◽  
Qing Zhang
Keyword(s):  
Limit Cycle ◽  
Finite Automata ◽  
Deterministic Finite Automata

Space-bounded OTMs and REG ∞

Computability ◽  
2021 ◽  
pp. 1-16
Author(s):  
Merlin Carl
Keyword(s):  
Complexity Theory ◽  
Turing Machine ◽  
Finite Automata ◽  
Regular Languages ◽  
The Other ◽  
Deterministic Finite Automata ◽  
Logarithmic Space ◽  
Working Space ◽  
Important Theorem

An important theorem in classical complexity theory is that REG = LOGLOGSPACE, i.e., that languages decidable with double-logarithmic space bound are regular. We consider a transfinite analogue of this theorem. To this end, we introduce deterministic ordinal automata (DOAs) and show that they satisfy many of the basic statements of the theory of deterministic finite automata and regular languages. We then consider languages decidable by an ordinal Turing machine (OTM), introduced by P. Koepke in 2005 and show that if the working space of an OTM is of strictly smaller cardinality than the input length for all sufficiently long inputs, the language so decided is also decidable by a DOA, which is a transfinite analogue of LOGLOGSPACE ⊆ REG; the other direction, however, is easily seen to fail.

scholarly journals SUBLINEARLY SPACE BOUNDED ITERATIVE ARRAYS

2010 ◽  
Vol 21 (05) ◽  
pp. 843-858 ◽  
Author(s):  
ANDREAS MALCHER ◽  
CARLO MEREGHETTI ◽  
BEATRICE PALANO
Keyword(s):  
Lower Bound ◽  
Computational Model ◽  
Regular Language ◽  
Finite Automata ◽  
Complexity Classes ◽  
Language Recognition ◽  
Deterministic Finite Automata ◽  
One Dimensional ◽  
Sequential Processing ◽  
Trade Offs

Iterative arrays (IAs) are a parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this paper, realtime-IAs with sublinear space bounds are used to recognize formal languages. The existence of an infinite proper hierarchy of space complexity classes between logarithmic and linear space bounds is proved. Some decidability questions on logarithmically space bounded realtime-IAs are investigated, and an optimal logarithmic space lower bound for non-regular language recognition on realtime-IAs is shown. Finally, some non-recursive trade-offs between space bounded realtime-IAs are emphasized.

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