Associate Professor Murray Elder
Associate Professor
School of Mathematical and Physical Sciences (Mathematics)
 Email:murray.elder@newcastle.edu.au
 Phone:(02) 4921 7472
Career Summary
Biography
Please see my research website for correct and uptodate information: https://sites.google.com/site/melderau
Qualifications
 Doctor of Philosophy, University of Melbourne
 Bachelor of Applied Science, La Trobe University
 Postgraduate Diploma, University of Melbourne
 Master of Science, University of Melbourne
Keywords
 Automata and formal languages
 Complexity theory
 Enumerative combinatorics
 Geometric group theory
Fields of Research
Code  Description  Percentage 

010105  Group Theory and Generalisations  70 
080201  Analysis of Algorithms and Complexity  15 
080203  Computational Logic and Formal Languages  15 
Professional Experience
UON Appointment
Title  Organisation / Department 

Associate Professor  University of Newcastle School of Mathematical and Physical Sciences Australia 
Academic appointment
Dates  Title  Organisation / Department 

1/01/2012  31/12/2015  ARC Future Fellow  University of Newcastle School of Mathematical and Physical Sciences Australia 
1/01/2011  31/12/2011  Lecturer  University of Newcastle School of Mathematical and Physical Sciences Australia 
1/01/2008  31/12/2010  Lecturer  The University of Queensland School of Mathematics and Physics Australia 
1/08/2006  1/01/2008  Assistant Professor  Stevens Institute of Technology Department of Mathematical Sciences United States 
1/01/2006  1/06/2006  Lecturer  University of Wollongong School of Mathematics and Applied Statistics Australia 
1/02/2004  1/08/2005  Research Fellow  University of St. Andrews Centre for Interdisciplinary Research in Computational Algebra United Kingdom 
1/09/2002  1/01/2004  Visiting Assistant Professor  Tufts University Mathematics United States 
1/09/2000  1/07/2002  Visiting Assistant Professor  Texas A&M University Mathematics United States 
Publications
For publications that are currently unpublished or inpress, details are shown in italics.
Book (1 outputs)
Year  Citation  Altmetrics  Link 

2005  Burillo J, Cleary S, Elder MJ, Taback J, Ventura E, Geometric Methods in Group Theory, American Mathematical Society, Providence, Rhode Island, 230 (2005) [A3] 
Journal article (37 outputs)
Year  Citation  Altmetrics  Link  

2016  Brough T, Ciobanu L, Elder MJ, Zetzsche G, 'Permutations of contextfree, ET0L and indexed languages', Discrete Mathematics & Theoretical Computer Science, 17 167178 (2016) [C1]  
2016 
Burton B, Elder MJ, Kalka A, Tillmann S, '2manifold recognition is in logspace', Journal of Computational Geometry, 7 7085 (2016) [C1]


2016 
Ciobanu L, Diekert V, Elder M, 'Solution sets for equations over free groups are EDT0L languages', International Journal of Algebra and Computation, 26 843886 (2016) Â© World Scientific Publishing Company.We show that, given an equation over a finitely generated free group, the set of all solutions in reduced words forms an effectively constru... [more] Â© World Scientific Publishing Company.We show that, given an equation over a finitely generated free group, the set of all solutions in reduced words forms an effectively constructible EDT0L language. In particular, the set of all solutions in reduced words is an indexed language in the sense of Aho. The language characterization we give, as well as further questions about the existence or finiteness of solutions, follow from our explicit construction of a finite directed graph which encodes all the solutions. Our result incorporates the recently invented recompression technique of Jez, and a new way to integrate solutions of linear Diophantine equations into the process. As a byproduct of our techniques, we improve the complexity from quadratic nondeterministic space in previous works to NSPACE(n log n) here.


2016 
Elder M, Taback J, 'Thompson's group F is 1counter graph automatic', Groups, Complexity, Cryptology, 8 2133 (2016) Â© 2016 by De Gruyter.It is not known whether Thompson's group F is automatic. With the recent extensions of the notion of an automatic group to graph automatic by Kharlampovich, ... [more] Â© 2016 by De Gruyter.It is not known whether Thompson's group F is automatic. With the recent extensions of the notion of an automatic group to graph automatic by Kharlampovich, Khoussainov and Miasnikov and then to Cgraph automatic by the authors, a compelling question is whether F is graph automatic or Cgraph automatic for an appropriate language class C. The extended definitions allow the use of a symbol alphabet for the normal form language, replacing the dependence on generating set. In this paper we construct a 1counter graph automatic structure for F based on the standard infinite normal form for group elements.


2015 
Burillo J, Elder M, 'Metric properties of BaumslagSolitar groups', International Journal of Algebra and Computation, 25 799811 (2015) [C1] Â© 2015 World Scientific Publishing Company.We compute estimates for the word metric of BaumslagSolitar groups in terms of the Britton's lemma normal form. As a corollary, we fin... [more] Â© 2015 World Scientific Publishing Company.We compute estimates for the word metric of BaumslagSolitar groups in terms of the Britton's lemma normal form. As a corollary, we find lower bounds for the growth rate for the groups BS(p, q) with 1 < p = q.


2015 
Banks C, Elder M, Willis GA, 'Simple groups of automorphisms of trees determined by their actions on finite subtrees', JOURNAL OF GROUP THEORY, 18 235261 (2015) [C1]


2015  Elder MJ, Lee G, Rechnitzer A, 'Permutations generated by a depth 2 stack and an infinite stack in series are algebraic', Electronic Journal of Combinatorics, 22 (2015) [C1]  
2015 
Elder MJ, Rechnitzer A, Janse van Rensberg EJ, 'Random Sampling of Trivial Words in Finitely Presented Groups', Experimental Mathematics, 24 391409 (2015) [C1]


2014 
Elder M, Taback J, 'Cgraph automatic groups', Journal of Algebra, 413 289319 (2014) [C1]


2014 
Elder M, Rechnitzer A, Janse van Rensburg EJ, Wong T, 'The cogrowth series for BS(N, N) is Dfinite', International Journal of Algebra and Computation, 24 171187 (2014) [C1]


2014  Davis N, Elder MJ, Reeves L, 'Noncontracting groups generated by (3,2)automata', Algebra and Discrete Mathematics, 17 2032 (2014) [C1]  
2013 
Elder M, Elston G, Ostheimer G, 'On groups that have normal forms computable in logspace', Journal of Algebra, 381 260281 (2013) [C1]


2012 
Bridson MR, Burillo J, Elder MJ, Sunic Z, 'On groups whose geodesic growth is polynomial', International Journal of Algebra and Computation, 22 (2012) [C1]


2012  Elder MJ, 'A short introduction to selfsimilar groups', Gazette of the Australian Mathematical Society, 39 125133 (2012) [C2]  
2012 
Elder MJ, Rechnitzer A, Wong T, 'On the cogrowth of Thompson's group F', Groups  Complexity  Cryptology, 4 301320 (2012) [C1]


2010 
Elder MJ, 'A lineartime algorithm to compute geodesics in solvable BaumslagSolitar groups', Illinois Journal of Mathematics, 54 109128 (2010) [C1]


2006 
Cleary S, Elder M, Taback J, 'Cone types and geodesic languages for lamplighter groups and Thompson's group F', JOURNAL OF ALGEBRA, 303 476500 (2006) [C1]


2006 
Albert MH, Elder M, Rechnitzer A, Westcott P, Zabrocki M, 'On the StanleyWilf limit of 4231avoiding permutations and a conjecture of arratia', ADVANCES IN APPLIED MATHEMATICS, 36 96105 (2006) [C1]


2006 
Elder M, 'Permutations generated by a stack of depth 2 and an infinite stack in series', ELECTRONIC JOURNAL OF COMBINATORICS, 13 (2006) [C1]


2005 
Elder M, 'A contextfree and a 1counter geodesic language for a BaumslagSolitar group', THEORETICAL COMPUTER SCIENCE, 339 344371 (2005) [C1]


2005 
Elder M, Hermiller S, 'Minimal almost convexity', JOURNAL OF GROUP THEORY, 8 239266 (2005) [C1]


2005 
Elder M, 'Regular geodesic languages and the falsification by fellow traveler property', ALGEBRAIC AND GEOMETRIC TOPOLOGY, 5 129134 (2005) [C1]


2004 
Elder MJ, 'A nonHopfian almost convex group', JOURNAL OF ALGEBRA, 271 1121 (2004) [C1]


2004 
Elder M, McCammond J, 'CAT(0) is an algorithmic property', GEOMETRIAE DEDICATA, 107 2546 (2004) [C1]


2003 
Elder M, McCammond J, Meier J, 'Combinatorial conditions that imply wordhyperbolicity for 3manifolds', TOPOLOGY, 42 12411259 (2003) [C1]


2003 
Elder MJ, 'The loop shortening property and almost convexity', GEOMETRIAE DEDICATA, 102 118 (2003) [C1]


2003 
Elder MJ, 'Patterns theory and geodesic automatic structure for a class of groups', INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 13 203230 (2003) [C1]


2002 
Elder MJ, 'Finiteness and the falsification by fellow traveler property', GEOMETRIAE DEDICATA, 95 103113 (2002) [C1]


2002 
Elder M, McCammond J, 'Curvature testing in 3dimensional metric polyhedral complexes', EXPERIMENTAL MATHEMATICS, 11 143158 (2002) [C1]


Show 34 more journal articles 
Conference (1 outputs)
Year  Citation  Altmetrics  Link  

2015 
Ciobanu L, Diekert V, Elder M, 'Solution sets for equations over free groups are EDT0L languages', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2015) [E1] Â© SpringerVerlag Berlin Heidelberg 2015.We show that, given a word equation over a finitely generated free group, the set of all solutions in reduced words forms an EDT0L langua... [more] Â© SpringerVerlag Berlin Heidelberg 2015.We show that, given a word equation over a finitely generated free group, the set of all solutions in reduced words forms an EDT0L language. In particular, it is an indexed language in the sense of Aho. The question of whether a description of solution sets in reduced words as an indexed language is possible has been open for some years [9,10], apparently without much hope that a positive answer could hold. Nevertheless, our answer goes far beyond: they are EDT0L, which is a proper subclass of indexed languages. We can additionally handle the existential theory of equations with rational constraints in free products Â¿1=i=sFi, where each Fi is either a free or finite group, or a free monoid with involution. In all cases the result is the same: the set of all solutions in reduced words is EDT0L. This was known only for quadratic word equations by [8], which is a very restricted case. Our general result became possible due to the recent recompression technique of Jez. In this paper we use a new method to integrate solutions of linear Diophantine equations into the process and obtain more general results than in the related paper [5]. For example, we improve the complexity from quadratic nondeterministic space in [5] to quasilinear nondeterministic space here. This implies an improved complexity for deciding the existential theory of nonabelian free groups: NSPACE(n log n). The conjectured complexity is NP, however, we believe that our results are optimal with respect to space complexity, independent of the conjectured NP.

Thesis / Dissertation (2 outputs)
Year  Citation  Altmetrics  Link 

2001  Elder MJ, Automaticity, almost convexity and falsification by fellow traveler properties of some finitely presented groups, The University of Melbourne (2001)  
1997  Elder MJ, Coxeter groups and the Moussong Complex, The University of Melbourne (1997) 
Grants and Funding
Summary
Number of grants  9 

Total funding  $1,382,720 
Click on a grant title below to expand the full details for that specific grant.
20161 grants / $422,552
The language complexity of problems in algebra and logic$422,552
Funding body: ARC (Australian Research Council)
Funding body  ARC (Australian Research Council) 

Project Team  Associate Professor Murray Elder, Dr Laura Ciobanu, Professor Volker Diekert 
Scheme  Discovery Projects 
Role  Lead 
Funding Start  2016 
Funding Finish  2018 
GNo  G1500017 
Type Of Funding  Aust Competitive  Commonwealth 
Category  1CS 
UON  Y 
20143 grants / $22,000
The logical complexity of problems in group theory$10,000
Funding body: University of Newcastle
Funding body  University of Newcastle 

Project Team  Associate Professor Murray Elder 
Scheme  Near Miss Grant 
Role  Lead 
Funding Start  2014 
Funding Finish  2014 
GNo  G1301377 
Type Of Funding  Internal 
Category  INTE 
UON  Y 
Faculty Visiting Fellowship 2014$10,000
Funding body: University of Newcastle  Faculty of Science & IT
Funding body  University of Newcastle  Faculty of Science & IT 

Project Team  Associate Professor Murray Elder 
Scheme  Visiting Fellowship 
Role  Lead 
Funding Start  2014 
Funding Finish  2014 
GNo  G1401050 
Type Of Funding  Internal 
Category  INTE 
UON  Y 
Faculty PVC Conference Assistance Grant 2014$2,000
Funding body: University of Newcastle  Faculty of Science & IT
Funding body  University of Newcastle  Faculty of Science & IT 

Project Team  Associate Professor Murray Elder 
Scheme  PVC Conference Assistance Grant 
Role  Lead 
Funding Start  2014 
Funding Finish  2014 
GNo  G1401186 
Type Of Funding  Internal 
Category  INTE 
UON  Y 
20131 grants / $24,000
DVC(R) Research Support for Future Fellow (FT11)$24,000
Funding body: University of Newcastle
Funding body  University of Newcastle 

Project Team  Associate Professor Murray Elder 
Scheme  Future Fellowship Support 
Role  Lead 
Funding Start  2013 
Funding Finish  2016 
GNo  G1301119 
Type Of Funding  Internal 
Category  INTE 
UON  Y 
20121 grants / $325,000
Theory and applications of symmetries of relational structures$325,000
Funding body: ARC (Australian Research Council)
Funding body  ARC (Australian Research Council) 

Project Team  Professor George Willis, Associate Professor Murray Elder 
Scheme  Discovery Projects 
Role  Investigator 
Funding Start  2012 
Funding Finish  2014 
GNo  G1100080 
Type Of Funding  Aust Competitive  Commonwealth 
Category  1CS 
UON  Y 
20113 grants / $589,168
Algorithmic and computational advances in geometric group theory$565,468
Funding body: ARC (Australian Research Council)
Funding body  ARC (Australian Research Council) 

Project Team  Associate Professor Murray Elder 
Scheme  Future Fellowships 
Role  Lead 
Funding Start  2011 
Funding Finish  2015 
GNo  G1100435 
Type Of Funding  Aust Competitive  Commonwealth 
Category  1CS 
UON  Y 
Generic complexity in computational topology: Breaking through the bottlenecks$20,700
Funding body: ARC (Australian Research Council)
Funding body  ARC (Australian Research Council) 

Project Team  Dr Benjamin Burton, Associate Professor Murray Elder, Dr Stephan Tillmann 
Scheme  Discovery Projects 
Role  Lead 
Funding Start  2011 
Funding Finish  2013 
GNo  G1001059 
Type Of Funding  Aust Competitive  Commonwealth 
Category  1CS 
UON  Y 
Efficient computations in infinite groups$3,000
Funding body: University of Newcastle
Funding body  University of Newcastle 

Project Team  Associate Professor Murray Elder 
Scheme  New Staff Grant 
Role  Lead 
Funding Start  2011 
Funding Finish  2011 
GNo  G1001071 
Type Of Funding  Internal 
Category  INTE 
UON  Y 
Research Supervision
Number of supervisions
Total current UON EFTSL
Current Supervision
Commenced  Level of Study  Research Title / Program / Supervisor Type 

2016  PhD 
Language Complexity of Problems in Algebra and Logic with Solution Sets PhD (Mathematics), Faculty of Science and Information Technology, The University of Newcastle Principal Supervisor 
2013  PhD 
On the Interconnectedness, via Random Walks, of Cogrowth Rates and the Folner Function PhD (Mathematics), Faculty of Science and Information Technology, The University of Newcastle Principal Supervisor 
News
ARC Discovery Projects funding success 2016
November 4, 2015
Dr Murray Elder, Dr Laura Ciobanu and Professor Volker Diekert have been awarded $417,000 in ARC Discovery Project funding commencing in 2016 for their research project The language complexity of problems in algebra and logic.
Associate Professor Murray Elder
Position
Associate Professor
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology
Focus area
Mathematics
Contact Details
murray.elder@newcastle.edu.au  
Phone  (02) 4921 7472 
Fax  (02) 4921 6898 
Link  Personal webpage 
Office
Room  V125 

Building  Mathematics Building 
Location  Callaghan University Drive Callaghan, NSW 2308 Australia 