Well-quasi-ordering hereditarily finite sets

References

• Abdulla , P. A. , Delzanno , G. and Van Begin , L. 2011 . A classification of the expressive power of well-structured transition systems . Inf. Comput. , 209 : 248 – 279 . (doi:10.1016/j.ic.2010.11.003)
   Web of Science ®Google Scholar
• Aczel , P. 1988 . Non-Well-Founded Sets , Vol. 14 , Stanford, CA : CSLI . CSLI Lecture Notes
   Google Scholar
• Bang-Jensen , J. and Gutin , G. 2000 . Digraphs Theory, Algorithms and Applications , 1 , Berlin : Springer-Verlag .
   Google Scholar
• Barwise , J. and Moss , L. 1991 . Hypersets . Math Intelligencer , 13 : 31 – 41 . (doi:10.1007/BF03028340)
   Web of Science ®Google Scholar
• Berwanger , D. , Dawar , A. , Hunter , P. and Kreutzer , S. 2006 . “ DAG-width and parity games ” . In STACS , Edited by: Durand , B. and Thomas , W. Vol. 3884 , 524 – 536 . Berlin, Heidelberg : Springer . Lecture Notes in Computer Science
   Google Scholar
• Berwanger , D. and Grädel , E. 2004 . “ Entanglement – A measure for the complexity of directed graphs with applications to logic and games ” . In LPAR , Edited by: Baader , F. and Voronkov , A. Vol. 3452 , 209 – 223 . Berlin, Heidelberg : Springer . Lecture Notes in Computer Science
   Google Scholar
• Chudnovsky , M. and Seymour , P. D. 2011 . A well-quasi-order for tournaments . J. Combin. Theory Ser. B , 101 : 47 – 53 . (doi:10.1016/j.jctb.2010.10.003)
   Web of Science ®Google Scholar
• D'Agostino , G. , Omodeo , E. , Policriti , A. and Tomescu , A. I. Mapping hypersets into numbers (extended abstract) . The 12th Italian Conference on Theoretical Computer Science . September , Camerino , Italy. Available at http://www.cs.unicam.it/ictcs2010/abstract/paper%2026.pdf (accessed 20 December 2012).
   Google Scholar
• Finkel , A. and Schnoebelen , P. 2001 . Well-structured transition systems everywhere! . Theoret. Comput. Sci. , 256 : 63 – 92 . (doi:10.1016/S0304-3975(00)00102-X)
   Web of Science ®Google Scholar
• Ganian , R. , Hlinený , P. , Kneis , J. , Meister , D. , Obdrzálek , J. , Rossmanith , P. and Sikdar , S. 2010 . “ Are there any good digraph width measures? ” . In IPEC , Edited by: Raman , V. and Saurabh , S. Vol. 6478 , 135 – 146 . Berlin, Heidelberg : Springer . Lecture Notes in Computer Science
   Google Scholar
• Higman , G. 1952 . Ordering by divisibility in abstract algebras . 3 : 326 – 336 .
   Google Scholar
• Hunter , P. and Kreutzer , S. 2008 . Digraph measures: Kelly decompositions, games, and orderings . Theoret. Comput. Sci. , 399 : 206 – 219 . (doi:10.1016/j.tcs.2008.02.038)
   Web of Science ®Google Scholar
• Johnson , T. , Robertson , N. , Seymour , P. D. and Thomas , R. 2001 . Directed tree-width . J. Combin. Theory Ser. B , 82 : 138 – 154 . (doi:10.1006/jctb.2000.2031)
   Web of Science ®Google Scholar
• Kreutzer , S. and Tazari , S. 2012 . “ Directed nowhere dense classes of graphs ” . In SODA , Edited by: Rabani , Y. l. 1552 – 1562 . Philadelphia : SIAM .
   Google Scholar
• Kruskal , J. B. 1960 . Well-quasi ordering, the tree theorem and Vászonyi's conjecture . Trans. Amer. Math. Soc. , 95 : 210 – 225 .
   Google Scholar
• Levy , A. 1979 . Basic Set Theory , Berlin : Springer .
   Google Scholar
• Nash-Williams , C. S.J.A. 1964 . “ On well-quasi-ordering trees ” . In Theory of Graphs and its Applications (Proc. Symp. Smolenice, 1963) , 83 – 84 . Prague : Publ. House Czechoslovak Acad. Sci .
   Google Scholar
• Piazza , C. and Policriti , A. 2004 . Ackermann encoding, bisimulations and OBDDs . Theory Pract. Log. Program. , 4 : 695 – 718 . (doi:10.1017/S1471068404002091)
   Web of Science ®Google Scholar
• Policriti , A. and Tomescu , A. I. Well-quasi-ordering hereditarily finite sets . Language and Automata Theory and Applications – 5th International Conference, LATA 2011 . May 26–31 , Tarragona , Spain. Edited by: Dediu , A. H. , Inenaga , S. and Martıin-Vide , C. Vol. 6638 , pp. 440 – 451 . Berlin, Heidelberg : Springer . Proceedings, Lecture Notes in Computer Science
   Google Scholar
• Robertson , N. and Seymour , P. 2004 . Graph minors. XX. Wagner's conjecture . J. Combin. Theory Ser. B , 92 : 325 – 357 . (doi:10.1016/j.jctb.2004.08.001)
   Web of Science ®Google Scholar
• Robertson , N. and Seymour , P. 2010 . Graph minors. XXIII. Nash-Williams's immersion conjecture . J. Combin. Theory Ser. B , 100 : 181 – 205 . (doi:10.1016/j.jctb.2009.07.003)
   Web of Science ®Google Scholar
• Tarau , P. Declarative modeling of finite mathematics . PPDP ’10: Proceedings of the 12th International ACM SIGPLAN Symposium on Principles and Practice of Declarative Programming . Hagenberg , Austria. Edited by: Kutsia , T. , Schreiner , W. and Fernández , M. pp. 131 – 142 . New York : ACM .
   Google Scholar