14,462 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
One-Way Reversible and Quantum Finite Automata with Advice
We examine the characteristic features of reversible and quantum computations
in the presence of supplementary external information, known as advice. In
particular, we present a simple, algebraic characterization of languages
recognized by one-way reversible finite automata augmented with deterministic
advice. With a further elaborate argument, we prove a similar but slightly
weaker result for bounded-error one-way quantum finite automata with advice.
Immediate applications of those properties lead to containments and separations
among various language families when they are assisted by appropriately chosen
advice. We further demonstrate the power and limitation of randomized advice
and quantum advice when they are given to one-way quantum finite automata.Comment: A4, 10pt, 1 figure, 31 pages. This is a complete version of an
extended abstract appeared in the Proceedings of the 6th International
Conference on Language and Automata Theory and Applications (LATA 2012),
March 5-9, 2012, A Coruna, Spain, Lecture Notes in Computer Science,
Springer-Verlag, Vol.7183, pp.526-537, 201
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
Liveness of Randomised Parameterised Systems under Arbitrary Schedulers (Technical Report)
We consider the problem of verifying liveness for systems with a finite, but
unbounded, number of processes, commonly known as parameterised systems.
Typical examples of such systems include distributed protocols (e.g. for the
dining philosopher problem). Unlike the case of verifying safety, proving
liveness is still considered extremely challenging, especially in the presence
of randomness in the system. In this paper we consider liveness under arbitrary
(including unfair) schedulers, which is often considered a desirable property
in the literature of self-stabilising systems. We introduce an automatic method
of proving liveness for randomised parameterised systems under arbitrary
schedulers. Viewing liveness as a two-player reachability game (between
Scheduler and Process), our method is a CEGAR approach that synthesises a
progress relation for Process that can be symbolically represented as a
finite-state automaton. The method is incremental and exploits both
Angluin-style L*-learning and SAT-solvers. Our experiments show that our
algorithm is able to prove liveness automatically for well-known randomised
distributed protocols, including Lehmann-Rabin Randomised Dining Philosopher
Protocol and randomised self-stabilising protocols (such as the Israeli-Jalfon
Protocol). To the best of our knowledge, this is the first fully-automatic
method that can prove liveness for randomised protocols.Comment: Full version of CAV'16 pape
Two-Way Automata Making Choices Only at the Endmarkers
The question of the state-size cost for simulation of two-way
nondeterministic automata (2NFAs) by two-way deterministic automata (2DFAs) was
raised in 1978 and, despite many attempts, it is still open. Subsequently, the
problem was attacked by restricting the power of 2DFAs (e.g., using a
restricted input head movement) to the degree for which it was already possible
to derive some exponential gaps between the weaker model and the standard
2NFAs. Here we use an opposite approach, increasing the power of 2DFAs to the
degree for which it is still possible to obtain a subexponential conversion
from the stronger model to the standard 2DFAs. In particular, it turns out that
subexponential conversion is possible for two-way automata that make
nondeterministic choices only when the input head scans one of the input tape
endmarkers. However, there is no restriction on the input head movement. This
implies that an exponential gap between 2NFAs and 2DFAs can be obtained only
for unrestricted 2NFAs using capabilities beyond the proposed new model. As an
additional bonus, conversion into a machine for the complement of the original
language is polynomial in this model. The same holds for making such machines
self-verifying, halting, or unambiguous. Finally, any superpolynomial lower
bound for the simulation of such machines by standard 2DFAs would imply LNL.
In the same way, the alternating version of these machines is related to L =?
NL =? P, the classical computational complexity problems.Comment: 23 page
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