An Implementation of Integer Presburger Arithmetic in a Math Education Tool

18 pages•Published: October 24, 2026

Abstract

An automata-theoretic implementation of a first-order theory of integers is discussed. It has addition, absolute values, minimum and maximum, and some bitwise operations, but lacks other multiplication than multiplication by a constant. The implementation is used in a tool that gives first- and second-year university students feedback on their answers to mathematics and computer science problems. The focus of this paper is on features of the tool supported by the implementation, and design and programming details that make it run sufficiently fast.

Keyphrases: bitwise operations, education tool, finite automata, integer presburger arithmetic

In: Stephan Schulz, Konstantin Korovin and Michael Rawson (editors). Proceedings of 16th International Workshop on the Implementation on Logics. Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning (short papers), vol 23, pages 133-150.

Links:	https://easychair.org/publications/paper/pzvK
	https://doi.org/10.29007/jlmh

BibTeX entry

@inproceedings{IWIL-2026:Implementation_Integer_Presburger_Arithmetic,
  author    = {Antti Valmari and Mika Hirvensalo},
  title     = {An Implementation of Integer Presburger Arithmetic in a Math Education Tool},
  booktitle = {Proceedings of 16th International Workshop on the Implementation on Logics. Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning (short papers)},
  editor    = {Stephan Schulz and Konstantin Korovin and Michael Rawson},
  series    = {Kalpa Publications in Computing},
  volume    = {23},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2515-1762},
  url       = {/publications/paper/pzvK},
  doi       = {10.29007/jlmh},
  pages     = {133-150},
  year      = {2026}}

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