# Recent publications of Marcel Jackson.

Note: arXiv links are to preprint versions where available.

### In Progress (who knows when)

L. Barto, L Ham and M. Jackson, Hardness for universal Horn classes and other implied constraint problems. (A little close since 2017.)

M. Jackson, The Finite Basis Problem is hard. (To be submitted soon.)

### Journal Articles: submitted

M. Jackson, Infinite irredundant axiomatisability for a finite monoid, 15 pp. arXiv

M. Jackson, Flexible satisfaction and a problem in semigroup theory, 33 pp. arXiv

L. Ham and M. Jackson, Finite model theory for pseudovarieties and universal algebra: preservation, definability and complexity, 34 pp. arXiv

### Journal Articles: in press and in print

T. Al Sulami and M, Jackson, Cyclic arithmetic and combinatorial operations, to appear in American Mathematical Monthly, 17pp.

P. Higgins and M. Jackson, Equationally defined classes of semigroups, to appear in Semigroup Forum 18 pp. arXiv

B. Al Juaid, M. Jackson, J. Koussas and T. Kowalski, Qualitative representations of chromatic algebras, Journal of Algebraic Combinatorics 58(1):157–182 (2023). arXiv

M. Ren, M. Jackson, X. Zhao and D. Lei, Flat extensions of groups and limit varieties of ai-semirings, Journal of Algebra 623: 64–85 (2023). arXiv

M. Jackson, M. Ren and X. Zhao, Nonfinitely based ai-semirings with finitely based semigroup reducts, Journal of Algebra 611:211–245 (2022). arXiv

M. Jackson and T. Stokes, Restriction in program algebra, Logic Journal of the IGPL DOI:10.1093/jigpal/jzac058, 35 pp (2022). arXiv

L. Ham, M. Jackson, M.P.H. Stumpf, Pathway dynamics can delineate the sources of transcriptional noise in gene expression, eLife 2021;10:e69324. biorXiv

M. Jackson and W.T. Zhang, From A to B to Z, Semigroup Forum 103 (2021) 165–190. arXiv

M. Jackson and T. Stokes, Override and update, Journal of Pure and Applied Algebra 225 (2021), 17pp. https://doi.org/10.1016/j.jpaa.2020.106532. arXiv

P.M. Higgins and M. Jackson, Algebras defined by equations, Journal of Algebra 555 (2020), 131–156. arXiv

R. Hirsch, M. Jackson and T. Kowalski, Algebraic foundations for qualitative calculi and networks, Theoretical Computer Science, 768 (2019) 99–116. arXiv

M. Jackson, Low growth equational complexity, Proc. Edinburgh Math. Soc., 62 (2019), 197–210. arXiv

M. Jackson and Sz. Mikulas, Domain and range for angelic and demonic compositions, Journal of Logical and Algebraic Methods in Programming 103 (2019), 62–78. arXiv

L. Ham and M. Jackson, Axiomatisability and hardness for universal Horn classes of hypergraphs, Algebra Universalis 78 (2018), 17pp arXiv

M. Jackson and E.W.H. Lee, Monoid varieties with extreme properties, Trans. Amer. Math. Soc., 370 (2018), 4785–4812. arXiv

A. Egri-Nagy, M. Jackson, J. Rhodes and B. Steinberg, On the atoms of algebraic lattices arising in q-theory, Internat. J. Algebra Comput. 27 (2017), 157–188. arXiv

M. Jackson, T. Kowalski and T. Niven, Complexity and polymorphisms for digraph constraint problems under some basic constructions, Internat. J. Algebra Comput., 26 (2016), 1395–1433. arXiv

R. Hirsch, M. Jackson and Sz. Mikulas, The algebra of functions with antidomain and range, J. Pure Appl. Algebra 220 (2016), no. 6, 2214–2239. arXiv

J. Bulin, D. Delic, M. Jackson and T. Niven, A finer reduction of constraint problems to digraphs, Logical Methods in Computer Science 11(4:18) (2015), 1–33. arXiv

C. Carvhalo, L. Egri, M. Jackson and T. Niven, On Maltsev digraphs, Electronic Journal of Combinatorics 22(1) (2015), #1.47.

M. Jackson and T. Stokes, Monoids with tests and the algebra of possibly non-halting programs, J. Log. Algeb. Program 84 (2015), 259–275. arXiv

M. Jackson, Natural dualities, nilpotence and projective planes, Algebra Universalis, 72 (2015), 65–85. arXiv

M. Jackson and T. Stokes, On representing semigroups with subsemilattices, J. Algebra 376 (2013), 228–260.

M. Jackson and B. Trotta, Constraint satisfaction, irredundant axiomatisability and continuous colouring, Studia Logica 101 (2013), 65–94.

R. Goldblatt and M. Jackson, Well structured program equivalence is undecidable, ACM Trans. Comput. Logic 13 (2012), Article 26, (8pp). arXiv

R. Hirsch and M. Jackson, Undecidable problems on representability as binary relations, J. Symbolic Logic 77 (2012), 1211–1244.

B. Davey, M. Jackson, J. Pitkethly and Cs. Szabo, Finite degree: algebras in general and semigroups in particular, Semigroup Forum 83 (2011), 89–110.

M. Jackson and T. Stokes, Modal restriction semigroups: towards an algebra of functions and deterministic computation, Internat. J. Algebra Comput. 21 (2011), 1053–1095.

M. Jackson and G. McNulty, The equational complexity of Lyndon's algebra, Algebra Universalis 65 (2011), 243–262.

M. Jackson and B. Trotta, The division relation: congruence conditions and axiomatisability, Comm. Algebra, 38 (2010), 534–566.

M. Jackson and T. Stokes, Semigroups with if-then-else and halting programs, Internat. J. Algebra Comput. 19 (2009), 937–961.

M. Jackson and M. Volkov, Undecidable problems for completely 0-simple semigroups, J. Pure Appl. Algebra 213 (2009), 1961–1978.

M. Jackson and T. Stokes, Partial maps with domain and range: extending Schein’s representation, Comm. Algebra 37 (2009), 2845–2870.

M. Jackson and M. Volkov, Relatively inherently nonfinitely q-based semigroups, Transactions of the American Mathematical Society 361 (2009), 2181–2206.

B. J. Gardner and M. Jackson, The Kuratowski Closure-Complement Theorem, New Zealand J. Math. 38 (2008), 9–34.

B. A. Davey, M. Jackson, M. Maróti and R. N. McKenzie, Principal and syntactic congruences in congruence-distributive and congruence-permutable varieties, J. Aust. Math. Soc. 85 (2008), 59–74.

D. M. Clark, B. A. Davey, M. Jackson and J. G. Pitkethly, The axiomatizability of topological prevarieties, Adv. Math. 218 (2008), 1604–1653.

J. Banks, G. Cairns, M. Jackson, M. Jerie, Y. Nikolayevski and T. Poole, On the definition of topology - a cautionary tale, Austral. Math. Soc. Gaz. 35 (2008), 195–202.

M. Jackson, Flat algebras and the translation of universal Horn logic to equational logic, J. Symbolic Logic 73 (2008), 90–128.

M. Jackson, Residual bounds for compact totally disconnected algebras, Houston J. Math. 34 (2008), 33–67.

B. A. Davey, M. Jackson, J. G. Pitkethly and M. R. Talukder, Natural dualities for semilattice-based algebras, Algebra Universalis 57 (2007), 463–490.

M. Jackson and T. Stokes, Identities in the algebra of partial maps, Internat. J. Algebra Comput. 16 (2006), 1131–1159.

M. Jackson and R. McKenzie, Interpreting graph colourability in finite semigroups, Internat. J. Algebra Comput. 16 (2006), 119–140.

M. Jackson, Finite semigroups with infinite irredundant identity bases, Internat. J. Algebra Comput. 15 (2005), 405–422.

M. Jackson, Finiteness properties of varieties and the restriction to finite algebras, Semigroup Forum 70 (2005), 159–187. Note that there is an error in the statement and proof of Prop 5.8. I have uploaded a correction here.

D. M. Clark, B. A. Davey, R. S. Freese and M. Jackson, Standard topological algebras: syntactic and principal congruences and profiniteness, Algebra Universalis 52 (2004), 343–376.

M. Jackson and T. Stokes, Semilattice pseudo-complements on semigroups, Comm. Algebra 32 (2004), 2895–2918.

M. Jackson, Semilattices with closure, Algebra Universalis 52 (2004), 1–37. Note that an error in Theorem 4.3 is corrected in Lemma 6.2 of the article [Davey, Jackson, Pitkethly, Talukder, Natural dualities for semilattice-based algebras, Algebra Univers. 57 (2007), 463–490] above.

M. Jackson, Dualisability of finite semigroups, Internat. J. Algebra Comput. 13 (2003) 481–497.

M. Jackson and T. Stokes, Agreeable semigroups, J. Algebra 266 (2003), 393–417.

M. Jackson, Generalising congruence regularity for varieties, Algebra Universalis 48 (2002), 249–252.

M. Jackson, On locally finite varieties with undecidable equational theory, Algebra Universalis 47 (2002), 1–6.

M. Jackson, Small inherently nonfinitely based finite semigroups, Semigroup Forum 64 (2002), 297–324.

M. Jackson and T. Stokes, An invitation to C-semigroups, Semigroup Forum 62 (2001), 279–310.

M. Jackson, On the finite basis problem for finite Rees quotients of free monoids, Acta Sci. Math. (Szeged) 67 (2001), 121–159.

M. Jackson and O. Sapir, Finitely based, finite sets of words, Internat. J. Algebra Comput. 10 (2000), 683–708.

M. Jackson, The embeddability of ring and semigroup amalgams is undecidable, J. Austral. Math. Soc. Ser. A 69 (2000), 272–286.

M. Jackson, Finite semigroups whose varieties have uncountably many subvarieties, J. Algebra 228 (2000), 512–535.

M. Jackson, Some undecidable embedding problems for finite semigroups, Proc. Edinburgh Math. Soc. (2) 42 (1999), 113–125.

M. G. Jackson, A note on HSI-algebras and counterexamples to Wilkie's identity, Algebra Universalis 36 (1996), 528–535.

### Book Chapters/Conference Proceedings

R. Hirsch, I. Hodkinson and M. Jackson, Undecidability of Algebra of Binary Relations, in Hajnal Andréka and István Németi on Unity of Science (2021), pp 267–287.

L. Ham and M. Jackson, All or Nothing: toward promise problem dichotomies for constraint problems, CP2017, LNCS10416, pp 139–156. arXiv

J. Bulin, D. Delic, M. Jackson and T. Niven, On the reduction of the CSP dichotomy conjecture to digraphs, CP2013, LNCS 8124, pp 184–199. arXiv

C. Mears, T. Niven, M. Jackson and M. Wallace, Proving symmetries by model transformation, CP2011, LNCS Vol. 6876/2011, pp. 591–605. (Authors in order of appearance on article.)

C. Carvhalo, L. Egri, M. Jackson and T. Niven, On Maltsev digraphs, Proceedings of the Sixth International Computer Science Symposium in Russia (CSR), A. Kulikov and N. Vereshchagin (Eds.): CSR 2011, LNCS 6651, pp. 181–194, 2011.

M. Jackson and M. Volkov, The algebra of adjacency patterns: Rees matrix semigroups with reversion, Gurevich Festschrift (A. Blass, N. Dershowitz, and W. Reisig Eds.), LNCS 6300, pp. 414–443, 2010. arXiv

M. Jackson and T. Stokes, Algebras of partial maps, Proceedings of the Special Interest Meeting on Semigroup Theory and Related Mathematics (Sydney, 2005), 26 pp. to appear. (***The delays in the publication of this conference proceedings now suggest that this article may never appear in published form. The article still contains numerous references, however there have been major advances on many of the items discussed in the article. A number of the open problems have been solved since 2005.)

M. Jackson, Syntactic semigroups and the finite basis problem, Structural Theory of Automata, Semigroups, and Universal Algebra (Montreal, 2003) (V. B. Kudryavtsev and I. G. Rosenberg, eds), NATO Sci. Ser. II: Math. Phys. Chem. 207, Springer, 2005, pp. 159–167.

M. Jackson, Paradoxes with dice and elections, Towards Excellence in Mathematics (Melbourne, 2004), Mathematical Association of Victoria, 2004, pp. 208–218.

### Other

(editor) General Algebra and Its Applications 2013 : Problem Session, Algebra Universalis 74 (2015), 9–15.