{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T04:10:48Z","timestamp":1751429448419,"version":"3.41.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2017,3,3]],"date-time":"2017-03-03T00:00:00Z","timestamp":1488499200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2017,3,3]]},"abstract":"<jats:p> We consider stochastic systems of equations of tree series, i.e., systems of equations whose right-hand sides are stochastic tree polynomials. We obtain their least solutions in arbitrary substochastic algebras, using both the [IO]- and OI-substitution mode. In the term algebra, we show that the consistency problem of the least [IO]- and OI-solutions is decidable, by reducing it to the consistency problem of stochastic context-free grammars. We prove a Kleene type theorem for the components of the least OI-solutions. The folklore Mezei-Wright result stating the coincidence of the components of least OI-solutions and behaviors of tree automata fails in the stochastic setup. As an application of our theory, we prove a Kleene theorem for the class of series generated by stochastic context-free grammars. <\/jats:p>","DOI":"10.3233\/fi-2017-1463","type":"journal-article","created":{"date-parts":[[2017,3,6]],"date-time":"2017-03-06T12:14:54Z","timestamp":1488802494000},"page":"143-177","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Stochastic Semantics"],"prefix":"10.1177","volume":"150","author":[{"given":"Symeon","family":"Bozapalidis","sequence":"first","affiliation":[{"name":"Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece. ,"}]},{"given":"George","family":"Rahonis","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece. ,"}]}],"member":"179","published-online":{"date-parts":[[2017,3,3]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2017-1463","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2017-1463","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:50:00Z","timestamp":1751367000000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2017-1463"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,3]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,3,3]]}},"alternative-id":["10.3233\/FI-2017-1463"],"URL":"https:\/\/doi.org\/10.3233\/fi-2017-1463","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"type":"print","value":"0169-2968"},{"type":"electronic","value":"1875-8681"}],"subject":[],"published":{"date-parts":[[2017,3,3]]}}}