Learning and Characterizing Fully-Ordered Lattice Automata

Dana Fisman, Sagi Saadon

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


Traditional automata classify words from a given alphabet as either good or bad. In many scenarios, in particular in formal verification, a finer classification is required. Fully-ordered lattice automata (FOLA) associate with every possible word a value from a finite set of values such as { 0, 1, 2, …, k}. In this paper we are interested in learning formal series that can be represented by FOLA. Such a series can be learned by a straight forward extension of the L algorithm. However, this approach does not take advantage of the special structure of a FOLA. In this paper we investigate FOLAs and provide a Myhill-Nerode characterization for FOLAs, which serves as a basis for providing a specialized algorithm for FOLAs, which we term FOL. We compare the performance of FOL to that of L on synthetically generated FOLA. Our experiments show that FOL outperforms L in the number of states of the obtained FOLA, the number of issued value queries (the extension of membership queries to the quantitative setting), and the number of issued equivalence queries.

Original languageEnglish
Title of host publicationAutomated Technology for Verification and Analysis - 20th International Symposium, ATVA 2022, Proceedings
EditorsAhmed Bouajjani, Lukáš Holík, Zhilin Wu
Place of PublicationCham
Number of pages17
ISBN (Electronic)9783031199929
ISBN (Print)9783031199912
StatePublished - 21 Oct 2022
Event20th International Symposium on Automated Technology for Verification and Analysis, ATVA 2022 - Virtual, Online
Duration: 25 Oct 202228 Oct 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13505 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference20th International Symposium on Automated Technology for Verification and Analysis, ATVA 2022
CityVirtual, Online

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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