{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:30Z","timestamp":1753889910887,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,11,30]],"date-time":"2017-11-30T00:00:00Z","timestamp":1512000000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,11,30]],"date-time":"2017-11-30T00:00:00Z","timestamp":1512000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,11,30]],"date-time":"2017-11-30T00:00:00Z","timestamp":1512000000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Given a logic presented in a sequent calculus, a natural question is that of equivalence of proofs: to determine whether two given proofs are equated by any denotational semantics, ie any categorical interpretation of the logic compatible with its cut-elimination procedure. This notion can usually be captured syntactically by a set of rule permutations.   Very generally, proofnets can be defined as combinatorial objects which provide canonical representatives of equivalence classes of proofs. In particular, the existence of proof nets for a logic provides a solution to the equivalence problem of this logic. In certain fragments of linear logic, it is possible to give a notion of proofnet with good computational properties, making it a suitable representation of proofs for studying the cut-elimination procedure, among other things.   It has recently been proved that there cannot be such a notion of proofnets for the multiplicative (with units) fragment of linear logic, due to the equivalence problem for this logic being Pspace-complete.   We investigate the multiplicative-additive (without unit) fragment of linear logic and show it is closely related to binary decision trees: we build a representation of proofs based on binary decision trees, reducing proof equivalence to decision tree equivalence, and give a converse encoding of binary decision trees as proofs. We get as our main result that the complexity of the proof equivalence problem of the studied fragment is Logspace-complete.<\/jats:p><jats:p>Comment: arXiv admin note: text overlap with arXiv:1502.01993<\/jats:p>","DOI":"10.23638\/lmcs-13(4:20)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:35:18Z","timestamp":1743701718000},"source":"Crossref","is-referenced-by-count":0,"title":["Multiplicative-Additive Proof Equivalence is Logspace-complete, via Binary Decision Trees"],"prefix":"10.23638","volume":"Volume 13, Issue 4","author":[{"given":"Marc","family":"Bagnol","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,11,30]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1707.00991v2","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1707.00991v2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:35:18Z","timestamp":1743701718000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/4111"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,30]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(4:20)2017","relation":{"is-same-as":[{"id-type":"arxiv","id":"1707.00991","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1707.00991","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2017,11,30]]},"article-number":"4111"}}