- A preview of this full-text is provided by Springer Nature.
- Learn more

Preview content only

Content available from Acta Informatica

This content is subject to copyright. Terms and conditions apply.

Acta Informatica (2018) 55:669–701

https://doi.org/10.1007/s00236-017-0306-5

ORIGINAL ARTICLE

Hierarchical information and the synthesis of distributed

strategies

Dietmar Berwanger1·Anup Basil Mathew1,2·

Marie van den Bogaard1

Received: 16 July 2016 / Accepted: 4 October 2017 / Published online: 17 October 2017

© Springer-Verlag GmbH Germany 2017

Abstract Inﬁnite games with imperfect information are known to be undecidable unless the

information ﬂow is severely restricted. One fundamental decidable case occurs when there

is a total ordering among players, such that each player has access to all the information that

the following ones receive. In this paper we consider variations of this hierarchy principle

for synchronous games with perfect recall, and identify new decidable classes for which the

distributed synthesis problem is solvable with ﬁnite-state strategies. In particular, we show

that decidability is maintained when the information hierarchy may change along the play,

or when transient phases without hierarchical information are allowed. Finally, we interpret

our result in terms of distributed system architectures.

Keywords Inﬁnite games ·Imperfect information ·Coordination ·Distributed systems ·

Automated synthesis

Mathematics Subject Classiﬁcation 91A06 ·68M14 ·93B50

1 Introduction

To realise systems that are correct by design is a persistent ambition in computing science.

The stake is particularly high for systems that interact with an unpredictable environment

over indeterminate time. Pioneering results in the area of synthesis, due to Büchi and Landwe-

ber [7], and Rabin [25], show that the task can be automatised for the case of monolithic

designs with correctness conditions speciﬁed by automata over inﬁnite objects—words or

trees representing computations. A most natural framework for representing and solving the

problem is in terms of inﬁnite games with perfect information over ﬁnite graphs, as described

by Pnueli and Rosner [23]orbyThomas[28].

BDietmar Berwanger

dwb@lsv.fr

1CNRS, ENS Paris-Saclay, LSV, Université Paris-Saclay, Paris, France

2The Institute of Mathematical Sciences, Chennai, India

123

Content courtesy of Springer Nature, terms of use apply. Rights reserved.