86 research outputs found
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
Pushdown Compression
The pressing need for eficient compression schemes for XML documents has
recently been focused on stack computation [6, 9], and in particular calls for
a formulation of information-lossless stack or pushdown compressors that allows
a formal analysis of their performance and a more ambitious use of the stack in
XML compression, where so far it is mainly connected to parsing mechanisms. In
this paper we introduce the model of pushdown compressor, based on pushdown
transducers that compute a single injective function while keeping the widest
generality regarding stack computation. The celebrated Lempel-Ziv algorithm
LZ78 [10] was introduced as a general purpose compression algorithm that
outperforms finite-state compressors on all sequences. We compare the
performance of the Lempel-Ziv algorithm with that of the pushdown compressors,
or compression algorithms that can be implemented with a pushdown transducer.
This comparison is made without any a priori assumption on the data's source
and considering the asymptotic compression ratio for infinite sequences. We
prove that Lempel-Ziv is incomparable with pushdown compressors
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
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
An Experiment in Ping-Pong Protocol Verification by Nondeterministic Pushdown Automata
An experiment is described that confirms the security of a well-studied class
of cryptographic protocols (Dolev-Yao intruder model) can be verified by
two-way nondeterministic pushdown automata (2NPDA). A nondeterministic pushdown
program checks whether the intersection of a regular language (the protocol to
verify) and a given Dyck language containing all canceling words is empty. If
it is not, an intruder can reveal secret messages sent between trusted users.
The verification is guaranteed to terminate in cubic time at most on a
2NPDA-simulator. The interpretive approach used in this experiment simplifies
the verification, by separating the nondeterministic pushdown logic and program
control, and makes it more predictable. We describe the interpretive approach
and the known transformational solutions, and show they share interesting
features. Also noteworthy is how abstract results from automata theory can
solve practical problems by programming language means.Comment: In Proceedings MARS/VPT 2018, arXiv:1803.0866
Pebble Minimization of Polyregular Functions
We show that a polyregular word-to-word function is regular if and only if
its output size is at most linear in its input size. Moreover a polyregular
function can be realized by: a transducer with two pebbles if and only if its
output has quadratic size in its input, a transducer with three pebbles if and
only if its output has cubic size in its input, etc. Moreover the
characterization is decidable and, given a polyregular function, one can
compute a transducer realizing it with the minimal number of pebbles. We apply
the result to mso interpretations from words to words. We show that mso
interpretations of dimension k exactly coincide with k-pebble transductions.Comment: The main result of the article is false. Counterexamples and more can
be found here: arXiv:2301.0923
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