Revisiting Synthesis for One-Counter Automata

05/03/2020
by   Guillermo A. Perez, et al.
0

One-counter automata are obtained by extending classical finite-state automata with a counter whose value can range over non-negative integers and be tested for zero. The updates and tests applicable to the counter can further be made parametric by introducing a set of integer-valued variables. We revisit the parameter synthesis problem for such automata. That is, we ask whether there exists a valuation of the parameters such that all infinite runs of the automaton satisfy some omega-regular property. The problem has been shown to be encodable in a restricted one-alternation fragment of Presburger arithmetic with divisibility. In this work (i) we argue that said fragment of the logic is unfortunately undecidable. Nevertheless, by reduction to a class of partial observation games, (ii) we prove the synthesis problem is decidable. Finally, (iii) we give a polynomial-space algorithm for the problem if parameters can only be used in tests, and not updates, of the counter.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

01/28/2021

Continuous One-Counter Automata

We study the reachability problem for continuous one-counter automata, C...
03/23/2018

A Curry-Howard Approach to Church's Synthesis

Church's synthesis problem asks whether there exists a finite-state stre...
09/07/2017

Beyond ωBS-regular Languages: ωT-regular Expressions and Counter-Check Automata

In the last years, various extensions of ω-regular languages have been p...
08/26/2020

Countdown games, and simulation on (succinct) one-counter nets

We answer an open complexity question by Hofman, Lasota, Mayr, Totzke (L...
04/10/2018

Counter Machines and Distributed Automata: A Story about Exchanging Space and Time

We prove the equivalence of two classes of counter machines and one clas...
01/03/2018

EXPSPACE-hardness of behavioural equivalences of succinct one-counter nets

We note that the remarkable EXPSPACE-hardness result in [Göller, Haase, ...
07/13/2018

Postselecting probabilistic finite state recognizers and verifiers

In this paper, we investigate the computational and verification power o...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.