arXiv subjects

Pierre-Alain Reynier

Publications and source records attributed to Pierre-Alain Reynier.

26 records · Page 2Linked to original sources

arXiv2017

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.

cs.FL↗

arXiv2016

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.

cs.FL↗

arXiv2016

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.

cs.FL↗

arXiv2014

On Streaming String Transducers and HDT0L Systems

Copyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. Cerny in 2010 as a one-way deterministic automata model to define transformations of finite strings. Copyless SST extend deterministic finite state automata with a set of registers in which to store intermediate output strings, and those registers can be combined and updated all along the run, in a linear manner, i.e., no register content can be copied on transitions. It is known that copyless SST capture exactly the class of MSO-definable string-to-string transformations, as defined by B. Courcelle, and are equi-expressive to deterministic two-way transducers. They enjoy good algorithmic properties. Most notably, they have decidable equivalence problem (in PSpace). In this paper, we show that they still have decidable equivalence problem even without the copyless restriction. The proof reduces to the HDT0L sequence equivalence problem, which is known to be decidable. We also show that this latter problem is as difficult as the SST equivalence problem, modulo linear time reduction.

cs.FL↗

arXiv2013

Expressiveness of Visibly Pushdown Transducers

Visibly pushdown transducers (VPTs) are visibly pushdown automata extended with outputs. They have been introduced to model transformations of nested words, i.e. words with a call/return structure. As trees and more generally hedges can be linearized into (well) nested words, VPTs are a natural formalism to express tree transformations evaluated in streaming. This paper aims at characterizing precisely the expressive power of VPTs with respect to other tree transducer models.

cs.FL↗

arXiv2013

From Two-Way to One-Way Finite State Transducers

Any two-way finite state automaton is equivalent to some one-way finite state automaton. This well-known result, shown by Rabin and Scott and independently by Shepherdson, states that two-way finite state automata (even non-deterministic) characterize the class of regular languages. It is also known that this result does not extend to finite string transductions: (deterministic) two-way finite state transducers strictly extend the expressive power of (functional) one-way transducers. In particular deterministic two-way transducers capture exactly the class of MSO-transductions of finite strings. In this paper, we address the following definability problem: given a function defined by a two-way finite state transducer, is it definable by a one-way finite state transducer? By extending Rabin and Scott's proof to transductions, we show that this problem is decidable. Our procedure builds a one-way transducer, which is equivalent to the two-way transducer, whenever one exists.

cs.FL↗

arXiv2012

Controllers with Minimal Observation Power (Application to Timed Systems)

We consider the problem of controller synthesis under imperfect information in a setting where there is a set of available observable predicates equipped with a cost function. The problem that we address is the computation of a subset of predicates sufficient for control and whose cost is minimal. Our solution avoids a full exploration of all possible subsets of predicates and reuses some information between different iterations. We apply our approach to timed systems. We have developed a tool prototype and analyze the performance of our optimization algorithm on two case studies.

eess.SY↗

arXiv2010

On Functionality of Visibly Pushdown Transducers

Visibly pushdown transducers form a subclass of pushdown transducers that (strictly) extends finite state transducers with a stack. Like visibly pushdown automata, the input symbols determine the stack operations. In this paper, we prove that functionality is decidable in PSpace for visibly pushdown transducers. The proof is done via a pumping argument: if a word with two outputs has a sufficiently large nesting depth, there exists a nested word with two outputs whose nesting depth is strictly smaller. The proof uses technics of word combinatorics. As a consequence of decidability of functionality, we also show that equivalence of functional visibly pushdown transducers is Exptime-Complete.

cs.FL↗