22 research outputs found
Finite automata with advice tapes
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.Comment: Corrected typo
Inkdots as advice for finite automata
We examine inkdots placed on the input string as a way of providing advice to
finite automata, and establish the relations between this model and the
previously studied models of advised finite automata. The existence of an
infinite hierarchy of classes of languages that can be recognized with the help
of increasing numbers of inkdots as advice is shown. The effects of different
forms of advice on the succinctness of the advised machines are examined. We
also study randomly placed inkdots as advice to probabilistic finite automata,
and demonstrate the superiority of this model over its deterministic version.
Even very slowly growing amounts of space can become a resource of meaningful
use if the underlying advised model is extended with access to secondary
memory, while it is famously known that such small amounts of space are not
useful for unadvised one-way Turing machines.Comment: 14 page
Verifying Time Complexity of Deterministic Turing Machines
We show that, for all reasonable functions , we can
algorithmically verify whether a given one-tape Turing machine runs in time at
most . This is a tight bound on the order of growth for the function
because we prove that, for and , there
exists no algorithm that would verify whether a given one-tape Turing machine
runs in time at most .
We give results also for the case of multi-tape Turing machines. We show that
we can verify whether a given multi-tape Turing machine runs in time at most
iff for some .
We prove a very general undecidability result stating that, for any class of
functions that contains arbitrary large constants, we cannot
verify whether a given Turing machine runs in time for some
. In particular, we cannot verify whether a Turing machine
runs in constant, polynomial or exponential time.Comment: 18 pages, 1 figur
Nondeterministic one-tape off-line Turing machines and their time complexity
In this paper we consider the time and the crossing sequence complexities of
one-tape off-line Turing machines. We show that the running time of each
nondeterministic machine accepting a nonregular language must grow at least as
n\log n, in the case all accepting computations are considered (accept
measure). We also prove that the maximal length of the crossing sequences used
in accepting computations must grow at least as \log n. On the other hand, it
is known that if the time is measured considering, for each accepted string,
only the faster accepting computation (weak measure), then there exist
nonregular languages accepted in linear time. We prove that under this measure,
each accepting computation should exhibit a crossing sequence of length at
least \log\log n. We also present efficient implementations of algorithms
accepting some unary nonregular languages.Comment: 18 pages. The paper will appear on the Journal of Automata, Languages
and Combinatoric