62 research outputs found
Synchronizing Deterministic Push-Down Automata Can Be Really Hard
The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time. In this paper, we extend this algorithmic question to deterministic automata beyond finite automata. We prove that the question of synchronizability becomes undecidable even when looking at deterministic one-counter automata. This is also true for another classical mild extension of regularity, namely that of deterministic one-turn push-down automata. However, when we combine both restrictions, we arrive at scenarios with a PSPACE-complete (and hence decidable) synchronizability problem. Likewise, we arrive at a decidable synchronizability problem for (partially) blind deterministic counter automata.
There are several interpretations of what synchronizability should mean for deterministic push-down automata. This is depending on the role of the stack: should it be empty on synchronization, should it be always the same or is it arbitrary? For the automata classes studied in this paper, the complexity or decidability status of the synchronizability problem is mostly independent of this technicality, but we also discuss one class of automata where this makes a difference
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 Equivalence and Uniformisation Problems for Finite Transducers
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper, we investigate stronger variants of inclusion, equivalence and sequential uniformisation, based on a general notion of transducer resynchronisation, and show their decidability. We also investigate the classes of finite-valued rational transductions and deterministic rational transductions, which are known to have a decidable equivalence problem. We show that sequential uniformisation is also decidable for them
Nondeterminism and Guarded Commands
The purpose of this paper is to discuss the relevance of nondeterminism in
computer science, with a special emphasis on Dijkstra's guarded commands
language.Comment: 34 pages. This is authors' version of Chapter 8 of the book K.R. Apt
and C.A.R. Hoare (editors), Edsger Wybe Dijkstra: His Life, Work, and Legacy,
volume 45 of ACM Books. ACM/Morgan & Claypool, 202
Decision Problems of Tree Transducers with Origin - Emmanuel Filiot
International audienc
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