696 research outputs found
On the Hierarchy of Block Deterministic Languages
A regular language is -lookahead deterministic (resp. -block
deterministic) if it is specified by a -lookahead deterministic (resp.
-block deterministic) regular expression. These two subclasses of regular
languages have been respectively introduced by Han and Wood (-lookahead
determinism) and by Giammarresi et al. (-block determinism) as a possible
extension of one-unambiguous languages defined and characterized by
Br\"uggemann-Klein and Wood. In this paper, we study the hierarchy and the
inclusion links of these families. We first show that each -block
deterministic language is the alphabetic image of some one-unambiguous
language. Moreover, we show that the conversion from a minimal DFA of a
-block deterministic regular language to a -block deterministic automaton
not only requires state elimination, and that the proof given by Han and Wood
of a proper hierarchy in -block deterministic languages based on this result
is erroneous. Despite these results, we show by giving a parameterized family
that there is a proper hierarchy in -block deterministic regular languages.
We also prove that there is a proper hierarchy in -lookahead deterministic
regular languages by studying particular properties of unary regular
expressions. Finally, using our valid results, we confirm that the family of
-block deterministic regular languages is strictly included into the one of
-lookahead deterministic regular languages by showing that any -block
deterministic unary language is one-unambiguous
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
Two-Way Visibly Pushdown Automata and Transducers
Automata-logic connections are pillars of the theory of regular languages.
Such connections are harder to obtain for transducers, but important results
have been obtained recently for word-to-word transformations, showing that the
three following models are equivalent: deterministic two-way transducers,
monadic second-order (MSO) transducers, and deterministic one-way automata
equipped with a finite number of registers. Nested words are words with a
nesting structure, allowing to model unranked trees as their depth-first-search
linearisations. In this paper, we consider transformations from nested words to
words, allowing in particular to produce unranked trees if output words have a
nesting structure. The model of visibly pushdown transducers allows to describe
such transformations, and we propose a simple deterministic extension of this
model with two-way moves that has the following properties: i) it is a simple
computational model, that naturally has a good evaluation complexity; ii) it is
expressive: it subsumes nested word-to-word MSO transducers, and the exact
expressiveness of MSO transducers is recovered using a simple syntactic
restriction; iii) it has good algorithmic/closure properties: the model is
closed under composition with a unambiguous one-way letter-to-letter transducer
which gives closure under regular look-around, and has a decidable equivalence
problem
Logics with rigidly guarded data tests
The notion of orbit finite data monoid was recently introduced by Bojanczyk
as an algebraic object for defining recognizable languages of data words.
Following Buchi's approach, we introduce a variant of monadic second-order
logic with data equality tests that captures precisely the data languages
recognizable by orbit finite data monoids. We also establish, following this
time the approach of Schutzenberger, McNaughton and Papert, that the
first-order fragment of this logic defines exactly the data languages
recognizable by aperiodic orbit finite data monoids. Finally, we consider
another variant of the logic that can be interpreted over generic structures
with data. The data languages defined in this variant are also recognized by
unambiguous finite memory automata
- …