scholarly journals Enumeration of minimal acyclic automata via generalized parking functions

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Jean-Baptiste Priez
Keyword(s):  
Finite Automata ◽  
Parking Functions ◽  
Deterministic Finite Automata ◽  
International Audience

International audience We give an exact enumerative formula for the minimal acyclic deterministic finite automata. This formula is obtained from a bijection between a family of generalized parking functions and the transitions functions of acyclic automata. On donne une formule d’énumération exacte des automates finites déterministes acycliques minimaux. Cetteformule s’obtient à partir d’une bijection entre une famille fonctions de parking généralisées et les fonctions detransitions des automates acycliques.

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.

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