Concise representations of regular languages by degree and probabilistic finite automata

1993 ◽  
Vol 26 (4) ◽  
pp. 379-395 ◽  
Author(s):  
Chandra M. R. Kintala ◽  
Kong -Yee Pun ◽  
Detlef Wotschke
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
Probabilistic Finite Automata

scholarly journals SOME LANGUAGES RECOGNIZED BY TWO-WAY FINITE AUTOMATA WITH QUANTUM AND CLASSICAL STATES

2012 ◽  
Vol 23 (05) ◽  
pp. 1117-1129 ◽  
Author(s):  
SHENGGEN ZHENG ◽  
DAOWEN QIU ◽  
LVZHOU LI
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
Reverse Order ◽  
Expected Time ◽  
Language L ◽  
Bounded Error ◽  
Probabilistic Finite Automata ◽  
Classical States

Two-way finite automata with quantum and classical states (2QCFA) were introduced by Ambainis and Watrous, and it was shown that 2QCFA have superiority over two-way probabilistic finite automata (2PFA) for recognizing some non-regular languages such as the language Leq = {anbn ∣ n ∈ N} and the palindrome language Lpal = {w ∈ {a,b}* ∣ w=wR}, where xR is x in the reverse order. It is interesting to find more languages like these that witness the superiority of 2QCFA over 2PFA. In this paper, we consider the language Lm = {xcy ∣ ∑ = {a,b,c},x,y ∈ {a,b}*, ∣x∣ = ∣y∣} that is similar to the middle language Lmiddle = {xay ∣ x,y ∈ {a,b}*, ∣x∣ = ∣y∣}. We prove that the language Lm show that Lm can be recognized by 2PFA with bounded error, but only in exponential expected time. Thus Lm is another witness of the fact that 2QCFA are more powerful than their classical counterparts.

Remarks on Four-Dimensional Probabilistic Finite Automata

2014 ◽  
Author(s):  
Makoto Sakamoto ◽  
Hiroshi Furutani ◽  
Yasuo Uchida ◽  
Makoto Nagatomo ◽  
Tuo Zhang ◽  
...  
Keyword(s):  
Finite Automata ◽  
Probabilistic Finite Automata

Decision Problems for Probabilistic Finite Automata on Bounded Languages

2013 ◽  
Vol 123 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Paul C. Bell ◽  
Vesa Halava ◽  
Mika Hirvensalo
Keyword(s):  
Finite Automata ◽  
Decision Problems ◽  
Probabilistic 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 On the Learnability and Usage of Acyclic Probabilistic Finite Automata

1998 ◽  
Vol 56 (2) ◽  
pp. 133-152 ◽  
Author(s):  
Dana Ron ◽  
Yoram Singer ◽  
Naftali Tishby
Keyword(s):  
Finite Automata ◽  
Probabilistic Finite Automata

scholarly journals Nondeterministic Syntactic Complexity

2021 ◽  
pp. 448-468
Author(s):  
Robert S. R. Myers ◽  
Stefan Milius ◽  
Henning Urbat
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
Syntactic Complexity ◽  
Deterministic Finite Automata ◽  
Syntactic Monoid ◽  
Nondeterministic Finite Automata ◽  
Structural Work ◽  
Algebraic Interpretation ◽  
Nondeterministic State

AbstractWe introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the ‘canonical boolean representation’ of the syntactic monoid. Equivalently, it is the least number of states of any subatomic nondeterministic acceptor. It turns out that essentially all previous structural work on nondeterministic state-minimality computes this measure. Our approach rests on an algebraic interpretation of nondeterministic finite automata as deterministic finite automata endowed with semilattice structure. Crucially, the latter form a self-dual category.

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