The sensing cost of monitoring and synthesis

Shaull Almagor, Denis Kuperberg, Orna Kupferman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations

Abstract

In [2], we introduced sensing as a new complexity measure for the complexity of regular languages. Intuitively, the sensing cost quantifies the detail in which a random input word has to be read by a deterministic automaton in order to decide its membership in the language. In this paper, we consider sensing in two principal applications of deterministic automata. The first is monitoring: we are given a computation in an on-line manner, and we have to decide whether it satisfies the specification. The second is synthesis: we are given a sequence of inputs in an on-line manner and we have to generate a sequence of outputs so that the resulting computation satisfies the specification. In the first, our goal is to design a monitor that handles all computations and minimizes the expected average number of sensors used in the monitoring process. In the second, our goal is to design a transducer that realizes the specification for all input sequences and minimizes the expected average number of sensors used for reading the inputs. We argue that the two applications require new and different frameworks for reasoning about sensing, and develop such frameworks. We focus on safety languages. We show that for monitoring, minimal sensing is attained by a monitor based on the minimal deterministic automaton for the language. For synthesis, however, the setting is more challenging: minimizing the sensing may require exponentially bigger transducers, and the problem of synthesizing a minimally-sensing transducer is EXPTIME-complete even for safety specifications given by deterministic automata.

Original languageAmerican English
Title of host publication35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2015
EditorsPrahladh Harsha, G. Ramalingam
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages380-393
Number of pages14
ISBN (Electronic)9783939897972
DOIs
StatePublished - 1 Dec 2015
Event35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2015 - Bangalore, India
Duration: 16 Dec 201518 Dec 2015

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume45
ISSN (Print)1868-8969

Conference

Conference35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2015
Country/TerritoryIndia
CityBangalore
Period16/12/1518/12/15

Bibliographical note

Publisher Copyright:
© Shaull Almagor, Denis Kuperberg, and Orna Kupferman;.

Keywords

  • Automata
  • Complexity
  • Minimization
  • Regular languages
  • Sensing
  • ω-regular languages

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