Research Papers
2010
 "Algebraic ordinals",
(coauthor: Z. Esik), to appear in Fundamenta Informaticae.

"A MezeiWright theorem for Categorical algebras",
(coauthor: Z. Ésik).
Theoretical Computer Science, 411 (2010) 341359.
2009
 "Cyclefree finite automata", (coauthors: Z.Esik, W. Kuich),
LNCS 1545 (2009), 112.

"Axiomatizing rational power series over natural numbers", (coauthors: Z. Ésik).
Information and Computation 207(2009), 793811.
2008

"On algebras with iteration", J. Logic and Computation,
vol 18, 6, December 2008, 10471085;
published electronically on October 1, 2008;
doi: 10.1093/logcom/exn035 (coauthors: J. Adamek, S. Milius)

"Partial Conway and iteration semirings", (coauthors: Z. Ésik, W. Kuich).
Fundamenta Informaticae, 86(2008), 1940
2007
 ``Regular and algebraic words and ordinals'', Procedings
of Algebra and Coalgebra in Computer Science, Bergen, Norway,
August 2007, Lecture Notes
in Computer Science 4624, 115. (coauthor: Z. Ésik).
Slides of talk.
2006
 "Omega completion of categorical algebras, with applications".
(coauthor: Z. Ésik). Extended abstract
in Procedings of IFIPTCS06.
Editied by G. Navarro,
L. Bertossi, Y. Kohayakawa. Springer, 2006.
Full paper:
Completing categorical algebras.
2005
 "The equational theory of regular words".
in
Information and Computation,
197/12 pp. 5589, 2005.
(coauthor: Z. Ésik).
Full paper.
2004
 "Axioms for regular words  extended abstract",
in: Proc. FST and TCS 03, Mumbai
LNCS 2914, Springer, 2003, 5061, and
Phoenix meeting of the American Mathematical Society,
Jan 610, 2004.
(coauthor: Z. Ésik).
 "Axiomatizing omega and omega op powers of words",
Theoretical Informatics and Applications.,
vol 38, 2004, 317.
(coauthor: Z. Ésik).
20012003
 "Deciding whether the frontier of a regular tree is scattered",
Fundamenta Informaticae, vol. 55(2) 2003, 121. (coauthor: Z. Ésik).
Reprint
 "Some remarks on regular words", BRICS Report Series 39, 2002 (coauthor: Z. Ésik).
 "An extension theorem with an application to
formal tree series", Journal of Automata, Languages and Combinatorics,
in a special issue "Selected papers of the workshop
Weighted Automata: Theory and Applications (Dresden, Germany, March 48,
2002)"; Vol. 8 (2003) Number 2. (coauthor: Z. Ésik).
Preprint
 "Unique guarded fixed points in an additive setting, Extended Abstract", Category Theory and Computer Science, 9th International Conference, CTCS '02. Proceedings, ENTCS 2002, vol. 69, Elsevier Science Pub., Rick Blute
and Peter Selinger, eds. (coauthor: Z. Ésik).
19982000
 "Long words: the theory of concatenation and power", Theoretical Computer Science, (12) 2001, Pages 533548. (coauthor: C. Choffrut)
Reprint
 "Iteration Algebras are not Finitely Axiomatizable",
LATIN 2000: Theoretical Informatics.
LNCS 1776, 367376, Springer, 2000. (coauthor: Z. Ésik)
 "Shuffle binoids", Informatique Théorique et Applications  RAIRO, vol 32, 1998, 175198. (coauthor: Z. Ésik)
Shuffle binoids
 "Iteration 2theories, Extended Abstract",
Algebraic Methodology and Software Technology,
6th International Conference AMAST 97,
LNCS 1349, Ed. M. Johnson, 3044. (coauthors: Z. Ésik, A. Labella and E.G. Manes).
19961998
 "The equational logic of fixed points" , Theoretical Computer Science, 179(1997), 160. (coauthor: Z. Ésik)
 "Two axiomatizations of a star semiring quasivariety",
Bulletin of the European Association for Theoretical Computer Science,
59, 1996, 150152. (coauthor: Z. Ésik)
 "Varieties Generated by Languages with Poset Operations", in Mathematical Foundations of Computer Science, 7, 1997, 701713. (coauthor: Z. Ésik)
 "Axiomatizing Concatenation and Shuffle in Languages", Infomation and Computation, 139, 6291, 1997.
And earlier.
 "Iteration algebras of finite state process behaviors", unpublished paper.
January, 1994 (coauthor: Z. Ésik)
Process behaviors
 "Nonfinite axiomatizability of shuffle inequalities", Proceedings of TAPSOFT/CAAP95, LNCS 915, 318333, 1995. (coauthor: Z. Ésik)
 "Free shuffle algebras in language varieties", in Theoretical Computer Science, 163(1996), pages 5598. Extended abstract in Proceedings of LATIN'95, pp. 99111, LNCS 911, edited by R. BaezaYates, E. Goles and P. Poblete. (coauthor: Z.Ésik)
 "Matrices, Machines and Behaviors", Research Report 949, Sydney University Mathematics Department. (coauthor: N. Sabadini, R.F.C. Walters), Applied Categorical Structures, 4(1996), 343360. Reprint
 "Some equational laws of initiality in 2ccc's", International Journal of Foundations of Computer Science, 6:1995, 95118. (coauthor: Z. Ésik).
 "Fixed point operations in ccc's", Theoretical Computer Science, 155:1996, 138. (Coauthor: Z. Ésik).
 "Solving polynomial fixed point equations", Proceedings of Mathematical Foundations of Computer Science '93, LNCS 841, SpringerVerlag, 1994, 5267. (coauthor: Z. Ésik)
 "Some quasivarieties of iteration theories", Proceedings of Mathematical Foundations of Programming Semantics 1993, LNCS 802, 378409 (coauthor: Z. Ésik).
Reprint
 "Equational theories of relations and regular sets, Extended abstract", in: Proc. conf. Words, Combinatorics and Semigroups, Kyoto, 1992, (coauthors: L. Bernátsky, Z. Ésik, and Gh. Stefanescu), Editors: Masami Ito and Helmut Jurgesen, Publisher: World ScientificPublishing Co. Pte. Ltd., 1994,40  48
 "Notes on Equational Theories of Relations", Algebra Universalis 33(1995), 98106. (coauthors: Z. Ésik, G. Stefanescu).
 "Equational axioms for the regular sets", Mathematical Structures in Computer Science, vol. 3 (1993), pp. 124 (coauthor: Z. Ésik)
 "Iteration Algebras", International Journal of Foundations of Computer Science, Vol. 3, No. 3, (1992) 245302. Erratum: International Journal of Foundations of Computer Science, vol. 4, No. 1, (1993), 99. Extended abstract in Lecture Notes in Computer Science, 493 (1991), 264274. (coauthor: Z. Ésik)
 "Program Correctness and Matricial Iteration Theories", Proceedings of Mathematical Foundations of Programming Semantics 1991 LNCS 598, 457475 (coauthor: Z. Ésik).
 "Matrix and matricial iteration theories of regular sets", Stevens Technical Report, 1990, (coauthor: Z. Ésik)
 "Iteration theories of Synchronization Trees", Proceedings of the Semantics for Concurrency Workshop, University of Leicester, July 1990, Information and Computation, vol. 102, No. 1 (1993), 155. (coauthors: Z. Ésik and D. Taubner)
 "Matrix and Matricial iteration theories, Part II," J. Computer and Syst. Sci., 46:3, 1993, 409439 (coauthor: Z. Ésik)
 "Matrix and Matricial iteration theories, Part I," J. Computer and Syst. Sci.,46:3, 1993, 381408 (coauthor: Z. Ésik)
 "Cayley iff Stone", Bulletin of the EATCS, 43, 1991, 159162 (coauthor: Z. Ésik)
 "FloydHoare logic in iteration theories," J. Assoc. Computing Machinery, vol. 38, No. 4 (1991) 887934 (coauthor: Z. Ésik)
 Review of S. Mac Lane Mathematics: Form and Function, Studia Logica, 1992
 Review of R. Wojicki's Theory of Logical Calculi, J. Symbolic Logic, vol 35, No. 3, September 1990, 13241326.
 "The equational logic of iterative processes," Proceedings of the FCT '89 conference; SpringerVerlag LNCS 380, (1989) 4757
 "Shuffle equations, parallel transition systems and equational Petri nets," Proceedings of the TAPSOFT '89 conference, SpringerVerlag Lecture Notes in Computer Science (Coauthor: K. Sutner)
 "A note on guarded theories," Theoretical Computer Science, 70 (1990) 7383.
 "A Cayley theorem for Boolean algebras," The American Mathematical Monthly, vol. 97 (1990), 831833 (coauthors: E. Manes, Z. Ésik).
 "Equational logic of circular data type specification," Theoretical Computer Science, vol 63, No. 3, (1989) 303331, (coauthor: Z. Ésik).
 "Varieties of iteration theories," SIAM J. of Computing, vol 17, No 5, Oct 1988, 939966 (coauthor: Z. Ésik).
 "A note on zero congruences," Acta Cybernetica, Tom. 8, Fasc. 1, (1987), 14 (coauthor: R. Tindell).
 "The alternation number and a dot hierarchy of regular sets," Acta Cybernetica, Tom 7, Fasc. 4 (1986) 355359.
 "Axiomatizing schemes and their behaviors," J. Computers and System Sciences, vol. 31, No. 3, (1985), 375393 (coauthor: Z. Ésik).
 "A logical characterization of observation equivalence," Theoretical Computer Science, 35 (1985) 4353 (coauthor: D. Troeger).
 "Many sorted algebraic theories with applications to abstract data types," Applications of algebra to language definition and compilation, M. Nivat and J. Reynolds (eds.) Cambridge University Press 1985, 134168 (coauthor E. Wagner)
 "Why algebraic theories," in Applications of algebra to language definition and compilation, M. Nivat and J. Reynolds (eds.) Cambridge University Press 1985 (coauthors: E. Wagner, J. Thatcher)
 "A note on profinite completions," IBM Research Report RC 11156, May, 1985 (coauthor: J. Wright).
 "Varieties of iteration theories," (Extended Abstract) Bulletin of the EATCS, October 1984, 5365 (coauthor: Z. Ésik).
 "Roman Suszko: a reminiscence," Studia Logica, XLIII, (1984), 4, 313.
 "Frontiers of oneletter languages," Acta Cybernetica, vol. 7, No. 1, (1984) 118.
 "Recursion and iteration in continuous theories," J. Computer and System Sci., Vol. 27, No. 2 (1983) 148164 (coauthors: J. Thatcher, E. Wagner, J. Wright)
 "Pvarieties: a signature free characterization of varieties of ordered algebras," J. Pure and Applied Algebra, 29 (1983) 1358 (coauthor: J. Wright)
 "Varieties of ifthenelse," SIAM J. Computing, vol. 12, no. 4 (1983) 677707 (coauthor: R. Tindell)
 "All solutions of a system of recursion equations in infinite trees and other contraction theories," J. Computer and System Sciences, Vol. 27, No. 2, (1983)
 "Elgot's analysis of monadic computation," Fundamenta Informaticae, vol. 2 (1982) 171186
 "Finitary quasivarieties," J. Pure and Applied Algebra, 25 (1982) 121154 (coauthor: J. Wright)
 "A note on the logic of signed equations," Studia Logica, vol XLI, no. 1 (1982) 7581.
 "Iterative and metric algebraic theories," Universal Algebra and Applications, Banach Center Publications, vol. 9, Polish Scientific Publishers, Warsaw (1982) 209224.
 "Easy solutions are hard to find," "CAAP '81", LNCS 112, 135146 (coauthor: D. Patterson)
 "Compatible orderings on the metric theory of trees," SIAM J. Computing, vol. 9, no. 4 (1980) 683691 (coauthor: R. Tindell)
 "Vector iteration in pointed iterative theories," SIAM J. Computing, vol.9, no. 3 (1980) 525540 (coauthors: C. Elgot, J. Wright)
 "All solutions of the iteration equation," SIAM J. Computing, vol. 9, no. 1 (1980) 2545 (coauthors: C. Elgot, J. Wright)
 "Algebraic and graph theoretic characterizations of structured flowchart schemes," Theoretical Computer Science, vol. 9, no. 3 (1979) 265286 (coauthor: R. Tindell)
 "The algebraic structure of rooted trees," J. Computer and System Sci., vol. 16, no. 3 (1978) 362399 (coauthors: C. Elgot, R. Tindell)
 "A note on consequences," Reports on Mathematical Logic, vol. 8, (1977) 39.
 "Scalar and vector iteration," J. Computer and System Sci., vol. 14, no. 2 (1977) 251256 (coauthors: J. Rutledge, S. Ginali)
 "Varieties of ordered algebras," J. Computer and System Sci., vol. 13, no. 2 (1976) 200212
 "The existence and construction of free iterative theories," J. Computer and System Sci., vol. 12 no. 3 (1976) 305318 (coauthor: C. Elgot)
 "Projective and inductive generation of abstract logics," Studia Logica, vol. 35, no. 3 (1976) 249255
 "A note on the predicatively definable sets of N. N. Nepeivoda," Zeit. Math. Logik, vol. 21, no. 3 (1976) 249431
 "Ultraproducts of SCI models", Bull. Section of Logic, Polish Acad. Sci., vol. 4, no. 1 (1975) 914 (coauthor: R. Suszko)
 "A representation theorem for the lattice of standard consequence operations," Studia Logica, vol. 34, no. 3 (1975) 235237.
 "Some theorems on structural consequence operations," Studia Logica, vol. 34, no. 1 (1975) 19
 "Vector and scalar iteration," IBM Research Report RC 4629, 1974. (coauthor: J. Rutledge)
 "On generalized logics," Studia Logica, vol. 33, no. 1 (1974), 6568.
 "A note on regular congruences," Colloquia Mathematica, vol. 29, no. 1 (1974) 2529.
 "A theorem on wellfinite standard consequence operations," Bull. Section of Logic, Polish Acad. Sci., vol. 2, no. 3 (1973) 159175
 "Extensions of Gödel's completeness theorem and the Löwenheim Skolem Theorem," Notre Dame J. Formal logic, vol. 14, no. 3 (1973) 408410
 "Classical abstract logics," Dissertationes Mathematicae, vol. CII (1973) (coauthor: D. Brown)
 "Structurality, substitution and completeness," J. Symbolic Logic, vol. 38, no. 2 (1973) 348 (coauthors: R. Suszko, D.Brown)
 "Model consequence operations and quasicomplete theories," Bull. Division of Logic, Polish Acad. Sci., vol. 1, no. 4 (1972) 1214
 "Investigations into the sentential calculus with identity connective," Notre Dame J. Formal Logic, vol. 13, no. 3 (1972), 289308 (coauthor: Roman Suszko)
 "Classical abstract logics I, II," Notices AMS, vol 18, no's 5,6 (1971) (coauthor: D. Brown)
 "Semantics for the SCI," Studia Logica, vol. 29 (1971) 7781 (coauthor: R. Suszko)
 "A model of the digital computer", Proc. Symposium XXI on Computers and Automata, Polytechnic Institute of Brooklyn, 1971, 539559 (coauthor: S. Amoroso)
 "Post complete finite algebras," J. Symbolic Logic, vol. 36, no. 4 (1971) 700
 "Some remarks on uniform halting problems," Zeitsch. Math. Logik, vol. 17, 1971, 281284
 "A completeness theorem for theories of kind W," Studia Logica, vol. 27 (1971), 4356
 "Some theorems on abstract logics," Algebra i Logika, vol. 9, no. 3 (1970) 274280 (coauthors: D. Brown, R. Suszko)
 "A note on abstract logics," Bull. Acad. Polonaise des Sci., serie des Sciences Math. astron. et phys., vol XVII, no. 3 (1970), 109110 (coauthors: D. Brown, R. Suszko)
 "The hyperprojective hierarchy," Zeitsch. Math. Logic und Grund. Mat., 16 (1970), 149164
 "Theories of kind W," Notices of the AMS, vol. 16, no. 3 (1969), 507.
 "A semicompleteness theorem," Notre Dame J. Formal Logic, X, No. 3 (1969), 303308
 "The hyperprojective hierarchy," Notices AMS, Vol. 15, no. 2 (1968), 343
 "A note on the arithmetical hierarchy," Notre Dame J. Formal Logic, IX, no.1 (1968) 8991
 "Rational Functions in Mathlab," Symbol Manipulation Languages and Techniques, North Holland (1968) 8697 (coauthors: M. Manove, C. Engleman)
Stephen Bloom
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