53 research outputs found
Aperiodic String Transducers
Regular string-to-string functions enjoy a nice triple characterization
through deterministic two-way transducers (2DFT), streaming string transducers
(SST) and MSO definable functions. This result has recently been lifted to FO
definable functions, with equivalent representations by means of aperiodic 2DFT
and aperiodic 1-bounded SST, extending a well-known result on regular
languages. In this paper, we give three direct transformations: i) from
1-bounded SST to 2DFT, ii) from 2DFT to copyless SST, and iii) from k-bounded
to 1-bounded SST. We give the complexity of each construction and also prove
that they preserve the aperiodicity of transducers. As corollaries, we obtain
that FO definable string-to-string functions are equivalent to SST whose
transition monoid is finite and aperiodic, and to aperiodic copyless SST
An automata characterisation for multiple context-free languages
We introduce tree stack automata as a new class of automata with storage and
identify a restricted form of tree stack automata that recognises exactly the
multiple context-free languages.Comment: This is an extended version of a paper with the same title accepted
at the 20th International Conference on Developments in Language Theory (DLT
2016
Degree of Sequentiality of Weighted Automata
Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the semantics is given by the set of weights of accepting runs. We focus on multi-sequential WA that are defined as finite unions of sequential WA. The problem we address is to minimize the size of this union. We call this minimum the degree of sequentiality of (the relation realized by) the WA.
For a given positive integer k, we provide multiple characterizations of relations realized by a union of k sequential WA over an infinitary finitely generated group: a Lipschitz-like machine independent property, a pattern on the automaton (a new twinning property) and a subclass of cost register automata. When possible, we effectively translate a WA into an equivalent union of k sequential WA. We also provide a decision procedure for our twinning property for commutative computable groups thus allowing to compute the degree of sequentiality. Last, we show that these results also hold for word transducers and that the associated decision problem is PSPACE
-complete
Church-Rosser Systems, Codes with Bounded Synchronization Delay and Local Rees Extensions
What is the common link, if there is any, between Church-Rosser systems,
prefix codes with bounded synchronization delay, and local Rees extensions? The
first obvious answer is that each of these notions relates to topics of
interest for WORDS: Church-Rosser systems are certain rewriting systems over
words, codes are given by sets of words which form a basis of a free submonoid
in the free monoid of all words (over a given alphabet) and local Rees
extensions provide structural insight into regular languages over words. So, it
seems to be a legitimate title for an extended abstract presented at the
conference WORDS 2017. However, this work is more ambitious, it outlines some
less obvious but much more interesting link between these topics. This link is
based on a structure theory of finite monoids with varieties of groups and the
concept of local divisors playing a prominent role. Parts of this work appeared
in a similar form in conference proceedings where proofs and further material
can be found.Comment: Extended abstract of an invited talk given at WORDS 201
Modular Descriptions of Regular Functions
We discuss various formalisms to describe string-to-string transformations.
Many are based on automata and can be seen as operational descriptions,
allowing direct implementations when the input scanner is deterministic.
Alternatively, one may use more human friendly descriptions based on some
simple basic transformations (e.g., copy, duplicate, erase, reverse) and
various combinators such as function composition or extensions of regular
operations.Comment: preliminary version appeared in CAI 2019, LNCS 1154
On Varieties of Ordered Automata
The Eilenberg correspondence relates varieties of regular languages to
pseudovarieties of finite monoids. Various modifications of this correspondence
have been found with more general classes of regular languages on one hand and
classes of more complex algebraic structures on the other hand. It is also
possible to consider classes of automata instead of algebraic structures as a
natural counterpart of classes of languages. Here we deal with the
correspondence relating positive -varieties of languages to
positive -varieties of ordered automata and we present various
specific instances of this correspondence. These bring certain well-known
results from a new perspective and also some new observations. Moreover,
complexity aspects of the membership problem are discussed both in the
particular examples and in a general setting
Recommended from our members
Containment and equivalence of weighted automata: Probabilistic and max-plus cases
This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain
Vectorial Languages and Linear Temporal Logic
International audienceDetermining for a given deterministic complete automaton the sequence of visited states while reading a given word is the core of important problems with automata-based solutions, such as approximate string matching. The main difficulty is to do this computation efficiently, especially when dealing with very large texts. Considering words as vectors and working on them using vectorial (parallel) operations allows to solve the problem faster than in linear time using sequential computations. In this paper, we show first that the set of vectorial operations needed by an algorithm representing a given automaton depends only on the language accepted by the automaton. We give precise characterizations of vectorial algorithms for star-free, solvable and regular languages in terms of the vectorial operations allowed. We also consider classes of languages associated with restricted sets of vectorial operations and relate them with languages defined by fragments of linear temporal logic. Finally, we consider the converse problem of constructing an automaton from a given vectorial algorithm. As a byproduct, we show that the satisfiability problem for some extensions of linear-time temporal logic characterizing solvable and regular languages is PSPACE-complete
- …