21 research outputs found
Multi-Head Finite Automata: Characterizations, Concepts and Open Problems
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg,
1966). Since that time, a vast literature on computational and descriptional
complexity issues on multi-head finite automata documenting the importance of
these devices has been developed. Although multi-head finite automata are a
simple concept, their computational behavior can be already very complex and
leads to undecidable or even non-semi-decidable problems on these devices such
as, for example, emptiness, finiteness, universality, equivalence, etc. These
strong negative results trigger the study of subclasses and alternative
characterizations of multi-head finite automata for a better understanding of
the nature of non-recursive trade-offs and, thus, the borderline between
decidable and undecidable problems. In the present paper, we tour a fragment of
this literature
Superiority of one-way and realtime quantum machines and new directions
In automata theory, the quantum computation has been widely examined for
finite state machines, known as quantum finite automata (QFAs), and less
attention has been given to the QFAs augmented with counters or stacks.
Moreover, to our knowledge, there is no result related to QFAs having more than
one input head. In this paper, we focus on such generalizations of QFAs whose
input head(s) operate(s) in one-way or realtime mode and present many
superiority of them to their classical counterparts. Furthermore, we propose
some open problems and conjectures in order to investigate the power of
quantumness better. We also give some new results on classical computation.Comment: A revised edition with some correction
Exact affine counter automata
Β© F. Blanchet-Sadri & S. Osborne. We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine counter automata but by neither 1-way deterministic pushdown automata nor realtime deterministic k-counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las Vegas affine finite automata. Lastly, we show that how a counter helps for affine finite automata by showing that the language MANYTWINS, which is conjectured not to be recognized by affine, quantum or classical finite state models in polynomial time, can be recognized by affine counter automata with one-sided bounded-error in realtime
On multi-head automata with restricted nondeterminism
In this work, we consider deterministic two-way multi-headautomata, the input heads of which are nondeterministically initialised, i.e., in every computation each input head is initially located at some nondeterministically chosen position of the input word. This model serves as an instrument to investigate restrictednondeterminism of two-way multi-headautomata. Our result is that, in terms of expressive power, two-way multi-headautomata with nondeterminism in form of nondeterministically initialising the input heads or with restrictednondeterminism in the classical way, i.e., in every accepting computation the number of nondeterministic steps is bounded by a constant, do not yield an advantage over their completely deterministic counter-parts with the same number of input heads. We conclude this paper with a brief application of this result
ΠΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΡΡΠ΅ΡΡΠΈΠΊΠΎΠ²ΡΡ ΠΌΠ°ΡΠΈΠ½ Π΄Π²ΡΡ Π³ΠΎΠ»ΠΎΠ²ΠΎΡΠ½ΡΠΌΠΈ Π°Π²ΡΠΎΠΌΠ°ΡΠ°ΠΌΠΈ
A method of modeling the Minsky counter machine behaviour by a two-head finite automaton is proposed.ΠΡΠΎΠ²ΠΎΠ΄ΠΈΡΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ°Π±ΠΎΡΡ ΡΡΠ΅ΡΡΠΈΠΊΠΎΠ²ΡΡ
ΠΌΠ°ΡΠΈΠ½ ΠΠΈΠ½ΡΠΊΠΎΠ³ΠΎ Ρ ΠΏΠΎΠΌΠΎΡΡΡ Π΄Π²ΡΡ
Π³ΠΎΠ»ΠΎΠ²ΠΎΡΠ½ΡΡ
Π°Π²ΡΠΎΠΌΠ°ΡΠΎΠ²
Characterizing co-NL by a group action
International audienceIn a recent paper, Girard proposes to use his recent construction of a geometry of interaction in the hyperfinite factor in an innovative way to characterize complexity classes. We begin by giving a detailed explanation of both the choices and the motivations of Girard's definitions. We then provide a complete proof that the complexity class co-NL can be characterized using this new approach. We introduce as a technical tool the non-deterministic pointer machine, a concrete model to computes algorithms