Finite automata with advice tapes
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This work defines a model of advised computation by finite automata where the advice is provided on a separate tape, and proves several separation results among variants, and demonstrates an infinite hierarchy of language classes recognized by automata with increasing advice lengths.Abstract:
We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed real-time, one-way, or two-way access, and the automaton is classical or quantum. We prove several separation results among these variants, demonstrate an infinite hierarchy of language classes recognized by automata with increasing advice lengths, and establish the relationships between this and the previously studied ways of providing advice to finite automata.read more
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BookDOI
Automata and quantum computing
TL;DR: This paper surveys various models of quantum finite automata and their properties, and provides some open questions and new directions for researchers.
BookDOI
Language and Automata Theory and Applications, 14th International Conference LATA 2020, Milan, Italy, March 4–6, 2020, Proceedings
TL;DR: This work surveys recent developments related to the Minimum Circuit Size Problem and proposes a strategy to address the problem.
Book ChapterDOI
Determinism and Nondeterminism in Finite Automata with Advice
TL;DR: This work considers the model of finite automata with advice introduced by Kucuk et al. and shows that there are languages, in particular the language of palindromes, that cannot be recognized by \(\text {DFA}\) regardless of the size of advice.
Journal ArticleDOI
Advice hierarchies among finite automata
Ahmet Bilal Uçan,A. C. Cem Say +1 more
TL;DR: In this paper , the authors examine the effects of supplying increasing amounts of trusted advice to a finite automaton, and demonstrate the existence of language hierarchies based on advice length, runtime, and advice tapes.
Proceedings ArticleDOI
Randomization in Non-Uniform Finite Automata.
Pavol Ďuriš,Rastislav Královič,Richard Královič,Dana Pardubská,Martin Pašen,Peter Rossmanith +5 more
TL;DR: It is shown that for unlimited advice, randomization is strictly stronger than determinism, and strictly weaker than non-determinism, but when the advice is restricted to polynomial length, the landscape changes: the expressive power of determinism and randomization does not change, but the power of non-Determinism is reduced to the extent that it becomes incomparable with randomization.
References
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Proceedings ArticleDOI
On the power of quantum finite state automata
A. Kondacs,John Watrous +1 more
TL;DR: It is proved that the class of languages recognizing by linear time, bounded error 2qfa's properly includes the regular languages, and 1-way and 2-way quantum finite state automata are introduced, which are the quantum analogues of deterministic, nondeterministic and probabilistic 1- way and2-way finite state Automata.
Journal ArticleDOI
The reduction of two-way automata to one-way automata
TL;DR: Rabin has proved that two-way finite automata, which are allowed to move in both directions along their input tape, are equivalent to one-way automata as far as the classification of input tapes is concerned.
Journal ArticleDOI
Unbounded-error quantum computation with small space bounds
Abuzer Yakaryilmaz,A. C. Cem Say +1 more
TL;DR: It turns out that these automata are equal in power to their probabilistic counterparts, and this fact does not change when the QFA model is augmented to allow general measurements and mixed states.
Journal ArticleDOI
Finite state verifiers I: the power of interaction
TL;DR: An investigation of interactive proof systems (IPSs) where the verifier is a 2-way probabilistic finite state automaton (2pfa) is initiated, and it is shown that IPSs with verifiers in the latter class are as powerful as IPSs where verifiers are polynomial-time Probabilistic Turing machines.