{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,28]],"date-time":"2022-04-28T08:48:56Z","timestamp":1651135736826},"reference-count":45,"publisher":"Elsevier BV","issue":"1-2","license":[{"start":{"date-parts":[[1999,8,1]],"date-time":"1999-08-01T00:00:00Z","timestamp":933465600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":5099,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theoretical Computer Science"],"published-print":{"date-parts":[[1999,8]]},"DOI":"10.1016\/s0304-3975(98)00317-x","type":"journal-article","created":{"date-parts":[[2003,4,7]],"date-time":"2003-04-07T19:40:02Z","timestamp":1049744402000},"page":"319-352","source":"Crossref","is-referenced-by-count":3,"title":["Simultaneous rigid E-unification and other decision problems related to the Herbrand theorem"],"prefix":"10.1016","volume":"224","author":[{"given":"Andrei","family":"Voronkov","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0304-3975(98)00317-X_BIB1","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1109\/TC.1976.1674698","article-title":"Refutations by matings","volume":"25","author":"Andrews","year":"1976","journal-title":"IEEE Trans. Comput."},{"key":"10.1016\/S0304-3975(98)00317-X_BIB2","series-title":"Arithmetic, Proof Theory and Computation Complexity","first-page":"20","article-title":"Note on the existence of most general semi-unifiers","volume":"vol. 23","author":"Baaz","year":"1993"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB3","first-page":"15","article-title":"Decidability of the universal theory of natural numbers with addition and divisibility","volume":"60","author":"Beltyukov","year":"1976"},{"issue":"4","key":"10.1016\/S0304-3975(98)00317-X_BIB4","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1145\/322276.322277","article-title":"On matrices with connections","volume":"28","author":"Bibel","year":"1981","journal-title":"J. Assoc. Comput. Mach."},{"key":"10.1016\/S0304-3975(98)00317-X_BIB5","series-title":"The Classical Decision Problem","author":"B\u00f6rger","year":"1997"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB6","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0052370","article-title":"The decidability of simultaneous rigid E-unification with one variable","author":"Degtyarev","year":"1997"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB7","series-title":"Rewriting Techniques and Applications, RTA'98","first-page":"181","article-title":"The decidability of simultaneous rigid E-unification with one variable","volume":"vol. 1379","author":"Degtyarev","year":"1998"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB8","article-title":"Simultaneous rigid E-unification is not so simple","author":"Degtyarev","year":"1995"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB9","series-title":"11th Annual IEEE Symp. on Logic in Computer Science (LICS'96)","first-page":"494","article-title":"Simultaneous rigid E-unification and related algorithmic problems","author":"Degtyarev","year":"1996"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB10","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-61377-3_38","article-title":"Simultaneous rigid E-unification is undecidable","author":"Degtyarev","year":"1995"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB11","series-title":"11th Annual IEEE Symp. on Logic in Computer Science (LICS'96)","first-page":"503","article-title":"Decidability problems for the prenex fragment of intuitionistic logic","author":"Degtyarev","year":"1996"},{"issue":"1\u20132","key":"10.1016\/S0304-3975(98)00317-X_BIB12","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/0304-3975(96)00092-8","article-title":"The undecidability of simultaneous rigid E-unification","volume":"166","author":"Degtyarev","year":"1996","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/S0304-3975(98)00317-X_BIB13","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0743-1066(84)90022-0","article-title":"On the sequential nature of unification","volume":"1","author":"Dwork","year":"1984","journal-title":"J. Logic Programm."},{"issue":"4","key":"10.1016\/S0304-3975(98)00317-X_BIB14","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1137\/0217046","article-title":"Parallel algorithms for term matching","volume":"17","author":"Dwork","year":"1988","journal-title":"SIAM J. Comput."},{"key":"10.1016\/S0304-3975(98)00317-X_BIB15","doi-asserted-by":"crossref","first-page":"795","DOI":"10.2307\/2275431","article-title":"Contraction-free sequent calculi for intuitionistic logic","volume":"57","author":"Dyckhoff","year":"1992","journal-title":"J. Symbolic Logic"},{"issue":"1","key":"10.1016\/S0304-3975(98)00317-X_BIB16","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1093\/jigpal\/6.1.17","article-title":"Decision procedures and model building in equational clause logic","volume":"6","author":"Ferm\u00fcller","year":"1998","journal-title":"Logic J. IGPL"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB17","series-title":"Proc. IEEE Conf. on Logic in Computer Science (LICS), IEEE Computer Society Press","first-page":"338","article-title":"Theorem proving using rigid E-unification: equational matings","author":"Gallier","year":"1987"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB18","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/0304-3975(81)90040-2","article-title":"The undecidability of the second-order unification problem","volume":"13","author":"Goldfarb","year":"1981","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/S0304-3975(98)00317-X_BIB19","article-title":"Some undecidable problems related to the Herbrand theorem","author":"Gurevich","year":"1997"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB20","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-63165-8_173","article-title":"Monadic simultaneous rigid E-unification and related problems","author":"Gurevich","year":"1997"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB21","series-title":"Automata, Languages and Programming. 24th Internat. Colloquium, ICALP'97","first-page":"154","article-title":"Monadic simultaneous rigid E-unification and related problems","volume":"vol. 1256","author":"Gurevich","year":"1997"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB22","series-title":"Logical Writings","author":"Herbrand","year":"1972"},{"issue":"1","key":"10.1016\/S0304-3975(98)00317-X_BIB23","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1093\/logcom\/3.1.63","article-title":"An O(n log n)-space decision procedure for intuitionistic propositional logic","volume":"3","author":"Hudelmaier","year":"1993","journal-title":"J. Logic Comput."},{"key":"10.1016\/S0304-3975(98)00317-X_BIB24","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1090\/S0002-9947-1978-0469886-1","article-title":"The Diophantine problem for addition and divisibility","volume":"235","author":"Lipshitz","year":"1978","journal-title":"Trans. Amer. Math. Soc."},{"issue":"1","key":"10.1016\/S0304-3975(98)00317-X_BIB25","first-page":"41","article-title":"Some remarks on the Diophantine problem for addition and divisibility","volume":"33","author":"Lipshitz","year":"1981","journal-title":"Bull. Soc. Math. Belg. S\u00e9r. B"},{"issue":"5","key":"10.1016\/S0304-3975(98)00317-X_BIB26","first-page":"588","article-title":"Universal extended theories of integers","volume":"16","author":"Mart'janov","year":"1977","journal-title":"Algebra i Logika"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB27","series-title":"Mathematical Theory of Logical Inference","first-page":"273","article-title":"Herbrand theorem (in Russian)","author":"Mints","year":"1967"},{"issue":"2","key":"10.1016\/S0304-3975(98)00317-X_BIB28","first-page":"273","article-title":"The Herbrand theorem for the predicate calculus with equality and function symbols","author":"Mints","year":"1969","journal-title":"Sov. Math. Dok."},{"key":"10.1016\/S0304-3975(98)00317-X_BIB29","first-page":"110","article-title":"A specialized form of derivation in Gentzen calculi and its applications (in Russian)","volume":"32","author":"Orevkov","year":"1974"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB30","series-title":"Computational Complexity","author":"Papadimitriou","year":"1994"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB31","doi-asserted-by":"crossref","DOI":"10.1007\/s002000050001","article-title":"Special cases and substitutes for rigid E-unification","author":"Plaisted","year":"1995"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB32","series-title":"Proc. 1st Internat. Workshop on Word Equations and Related Topics","article-title":"Makanin's algorithm: two improvements and a generalization","volume":"vol. 572","author":"Schulz","year":"1990"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB33","article-title":"On computational complexity of basic decision problems of finite tree automata","author":"Veanes","year":"1996"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB34","article-title":"On simultaneous rigid E-unification","author":"Veanes","year":"1997"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB35","series-title":"Computational Logic and Proof Theory. 5th Kurt G\u00f6del Colloquium, KGC'97","first-page":"305","article-title":"The undecidability of simultaneous rigid E-unification with two variables","volume":"vol. 1289","author":"Veanes","year":"1997"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB36","doi-asserted-by":"crossref","DOI":"10.1109\/LICS.1998.705663","article-title":"The relation between second-order unification and simultaneous rigid E-unification","author":"Veanes","year":"1998"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB37","article-title":"On Herbrand skeletons","author":"Voda","year":"1995"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB38","series-title":"Theorem Proving with Analytic Tableaux and Related Methods. 5th Internat. Workshop, TABLEAUX '96","first-page":"312","article-title":"Proof search in intuitionistic logic based on constraint satisfaction","volume":"vol. 1071","author":"Voronkov","year":"1996"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB39","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-61208-4_20","article-title":"Proof-search in intuitionistic logic based on the constraint satisfaction","author":"Voronkov","year":"1996"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB40","series-title":"Automated Deduction \u2014 CADE-13","first-page":"32","article-title":"Proof search in intuitionistic logic with equality, or back to simultaneous rigid E-unification","volume":"vol. 1104","author":"Voronkov","year":"1996"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB41","first-page":"11","article-title":"The ground-negative fragment of first-order logic is \u03a02p-complete","author":"Voronkov","year":"1997","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB42","first-page":"114","article-title":"Strategies in rigid-variable methods","volume":"vol. 1","author":"Voronkov","year":"1997"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB43","doi-asserted-by":"crossref","DOI":"10.1109\/LICS.1998.705662","article-title":"Herbrand's theorem, automated reasoning and semantic tableaux","author":"Voronkov","year":"1998"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB44","first-page":"28","article-title":"Proof-search in intuitionistic logic with equality, or back to simultaneous rigid E-unification","author":"Voronkov","year":"1998","journal-title":"J. Automat. Reason"},{"key":"10.1016\/S0304-3975(98)00317-X_BIB45","series-title":"Proc. Conf. on Fifth Generation Computer Systems, ICOT","first-page":"235","article-title":"On parallel computational complexity of unification","author":"Yasuura","year":"1984"}],"container-title":["Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S030439759800317X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S030439759800317X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T13:21:35Z","timestamp":1555420895000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S030439759800317X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,8]]},"references-count":45,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[1999,8]]}},"alternative-id":["S030439759800317X"],"URL":"https:\/\/doi.org\/10.1016\/s0304-3975(98)00317-x","relation":{},"ISSN":["0304-3975"],"issn-type":[{"value":"0304-3975","type":"print"}],"subject":[],"published":{"date-parts":[[1999,8]]}}}