5,618 research outputs found
Deterministic recognizability of picture languages with Wang automata
special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to ApplicationsInternational audienceWe present a model of automaton for picture language recognition, called Wang automaton, which is based on labeled Wang tiles. Wang automata combine features of both online tessellation acceptors and 4-way automata: as in online tessellation acceptors, computation assigns states to each picture position; as in 4-way automata, the input head visits the picture moving from one pixel to an adjacent one, according to some scanning strategy. Wang automata recognize the class REC, i.e. they are equivalent to tiling systems or online tessellation acceptors, and hence strictly more powerful than 4-way automata. We also introduce a natural notion of determinism for Wang automata, and study the resulting class, extending the more traditional approach of diagonal-based determinism, used e. g. by deterministic tiling systems. In particular, we prove that the concept of row (or column) ambiguity defines the class of languages recognized by Wang automata directed by boustrophedonic scanning strategies
Strategies to scan pictures with automata based on Wang tiles
Wang automata are devices for picture language recognition recently introduced by us, which characterize the class REC of recognizable picture languages. Thus, Wang automata are equivalent to tiling systems or online tessellation acceptors, and are based like Wang systems on labeled Wang tiles. The present work focus on scanning strategies, to prove that the ones Wang automata are based on are those following four kinds of movements: boustrophedonic, ``L-like'', ``U-like'', and spirals
Algebraic properties of structured context-free languages: old approaches and novel developments
The historical research line on the algebraic properties of structured CF
languages initiated by McNaughton's Parenthesis Languages has recently
attracted much renewed interest with the Balanced Languages, the Visibly
Pushdown Automata languages (VPDA), the Synchronized Languages, and the
Height-deterministic ones. Such families preserve to a varying degree the basic
algebraic properties of Regular languages: boolean closure, closure under
reversal, under concatenation, and Kleene star. We prove that the VPDA family
is strictly contained within the Floyd Grammars (FG) family historically known
as operator precedence. Languages over the same precedence matrix are known to
be closed under boolean operations, and are recognized by a machine whose pop
or push operations on the stack are purely determined by terminal letters. We
characterize VPDA's as the subclass of FG having a peculiarly structured set of
precedence relations, and balanced grammars as a further restricted case. The
non-counting invariance property of FG has a direct implication for VPDA too.Comment: Extended version of paper presented at WORDS2009, Salerno,Italy,
September 200
Complexity of Two-Dimensional Patterns
In dynamical systems such as cellular automata and iterated maps, it is often
useful to look at a language or set of symbol sequences produced by the system.
There are well-established classification schemes, such as the Chomsky
hierarchy, with which we can measure the complexity of these sets of sequences,
and thus the complexity of the systems which produce them.
In this paper, we look at the first few levels of a hierarchy of complexity
for two-or-more-dimensional patterns. We show that several definitions of
``regular language'' or ``local rule'' that are equivalent in d=1 lead to
distinct classes in d >= 2. We explore the closure properties and computational
complexity of these classes, including undecidability and L-, NL- and
NP-completeness results.
We apply these classes to cellular automata, in particular to their sets of
fixed and periodic points, finite-time images, and limit sets. We show that it
is undecidable whether a CA in d >= 2 has a periodic point of a given period,
and that certain ``local lattice languages'' are not finite-time images or
limit sets of any CA. We also show that the entropy of a d-dimensional CA's
finite-time image cannot decrease faster than t^{-d} unless it maps every
initial condition to a single homogeneous state.Comment: To appear in J. Stat. Phy
Remarks on separating words
The separating words problem asks for the size of the smallest DFA needed to
distinguish between two words of length <= n (by accepting one and rejecting
the other). In this paper we survey what is known and unknown about the
problem, consider some variations, and prove several new results
Infinite Networks, Halting and Local Algorithms
The immediate past has witnessed an increased amount of interest in local
algorithms, i.e., constant time distributed algorithms. In a recent survey of
the topic (Suomela, ACM Computing Surveys, 2013), it is argued that local
algorithms provide a natural framework that could be used in order to
theoretically control infinite networks in finite time. We study a
comprehensive collection of distributed computing models and prove that if
infinite networks are included in the class of structures investigated, then
every universally halting distributed algorithm is in fact a local algorithm.
To contrast this result, we show that if only finite networks are allowed, then
even very weak distributed computing models can define nonlocal algorithms that
halt everywhere. The investigations in this article continue the studies in the
intersection of logic and distributed computing initiated in (Hella et al.,
PODC 2012) and (Kuusisto, CSL 2013).Comment: In Proceedings GandALF 2014, arXiv:1408.556
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