Research papers

Research Papers

A New Derivative for Functions

Weak topology and differentiable operator for Lipschitz maps Extended Abstract in Proceedings of Twenty-Third Annual IEEE Symposium on LOGIC IN COMPUTER SCIENCE (LICS 2008)

A continuous derivative for real-valued functions New Computational Paradigms, Changing Conceptions of What is Computable, eds. S.B. Cooper, B. Lowe, A. Sorbi, pp. 493-519, Springer, New York, 2008.

This paper is dedicated to the historical memory of Sharaf al-din Tusi (d. 1213), the Iranian mathematician who was the first to use the derivative systematically to solve for roots of cubic polynomials and find their maxima. Persian description

Data Types for Lebesgue Integration

A computable approach to measure and integration theory Information and Computation Volume 207, Issue 5, May 2009, Pages 642-659

This paper is dedicated to the historical memory of Jamshid Kashani (d. 1429), the Iranian mathematician who was the first to use the recursive fixed point method in analysis with which he computed the sine of one degree correct up to 9 sexagesimal places; he also computed the number pi correct up to 16 decimal places

Hybrid systems

Denotational Semantics of Hybrid Automata (with D. Pattinson) In Proceedings of Foundations of Software Science and Computation Structures: 9th International Conference, FOSSACS 2006 Lecture Notes in Computer Science Volume 3921 pp.231-245 March, 2006

Data-types for Differential Calculus and Ordinary Differential Equations

	Inverse and Implicit Functions in Domain Theory (with D. Pattinson) In Proceedings of LICS 2005.
	A Computational Model for Multi-Variable Differential Calculus (with A. Lieutier and D. Pattinson) In Proceedings of FOSSACS 2005.
	A domain theoretic account of Euler's method for Solving Initial Value Problems (with D. Pattinson) In Proceedings of PARA 2004
	A domain theoretic account of Picard's theorem (with D. Pattinson) In Proceedings of ICALP 2004.
	Domain-theoretic Solution of Differential Equations (Scalar Fields) (with M. Krznaric and A. Lieutier).

Domain Theory and Differential Calculus (Functions of one variable) (with Andre Lieutier).
Mathematical Structures in Computer Science, Volume 14, Issue 06, Dec 2004, pp 771-802. (Extended abstract in Proceedings of IEEE Symposium on Logic in Computer Science (LICS) 2002.)

Quantum Computation

An Extension of Gleason's Theorem for Quantum Computation International Journal of Theoretical Physics 43 (7-8): 1827-1840, August 2004

Lecture Notes on Exact Computation

Computing with real numbers: (i) LFT approach to real computation, (ii) Domain-theoretic model of computational geometry (with Reinhold Heckmann) In Gilles Barthe, Peter Dybjer, Luis Pinto, and Joao Saraiva, editors, LNCS, Springer, 2002.

Computational Geometry and Soild Modelling

	Computability in Computational Geometry (with with Ali A. Khanban and Andre Lieutier), Lecture Notes in Computer Science, Volume 3526/2005, pages 117-127 .
	Computational Geometry with Imprecise Input Data (with with Ali A. Khanban and Andre Lieutier).
	Foundation of a Computable Solid Modelling (with Andre Lieutier). Theoretical Computer Science. Volume 284, Issue 2, Pages 319-345 (28 July 2002)(Extended abstract in Proceedings of ACM's Symposium on Solid Modeling'99, ACM, 1999.)
	Computing Delaunay triangulation with imprecise data (with Ali A. Khanban). Proceedings of the 15th Canadian Computational Geometry Conference, 2003.
	Computability of Partial Delaunay Triangulation and Voronoi Diagram (with Ali A. Khanban and Andre Lieutier). Electronic Notes in Theoretical Computer Science, Volume 66, Issue 1, 2002 (Proceedings of the 5th CCA Workshop, July 2002.)
	Convex Hull in a New Model of Computation (with Andre Lieutier and Elham Kashefi). Proceedings of the 13th Canadian Conference on Computational Geometry University of Waterloo, August 13-15, 2001.

Survey Article

Domains for Computation in Mathematics, Physics and Exact Real Arithmetic.
Bulletin of Symbolic Logic, 3(4), (1997), 401-452.

Exact Real Number Computation

	A Domain-theoretic Approach to Real Number Computation (with Philipp Sünderhauf). Theoretical Computer Science, 210, (1998), 73-98.
	A New representation of for Exact real Numbers (with Peter John Potts). Electronic Notes in Theoretical Computer Science 6, (1997).
	Integration in Real PCF (with Martin Escardo). Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science, (1996), 382-393, IEEE Computer Society; full paper to appear in Information and Computation.
	Exact Real Computer Arithmetic (with Peter John Potts). Department of Computing Technical Report DOC 97/9, Imperial College, (1997).
	Semantics of Exact Arithmetic (with Peter John Potts and Martin Escardo). Twelfth Annual IEEE Symposium on Logic in Computer Science, (1997), IEEE Computer Society.
	Two Algorithms for Root Finding in Exact real Arithmetic (with Fabien Rico). Third Real Numbers and Computers Conference, 27-44, (1998).
	Lazy computation with exact real numbers (with Peter John Potts and Philipp Sünderhauf). Proceedings of the Third ACM SIGPLAN International Confrence on Functional Programming, 185-194, (1998), ACM.
	Numerical integration with Exact Arithmetic (with Marko Krznaric). Proceedings of ICALP'99.
	The PhD Thesis of Peter John Potts.
	Miranda Implementation of Exact Real Arithmetic Using Mobius Transformation.

Domain Theory in Computational Topology,
Dynamical Systems and Measure/Integration Theory

	Dynamical systems, Measures and Fractals via Domain Theory. Information and Computation 120(1), (1995), 32-48.
	Domain Theory and Integration. Theoretical Computer Science 151, (1995), 163-193.
	Power Domains and Iterated Function Systems. Information and Computation 124, (1996), 182-197.
	When Scott is Weak on the Top. Mathematical Structures in Computer Science 7, (1997), 401-417.
	A Computational Model for Metric Spaces (with Reinhold Heckmann). Theoretical Computer Science 193, (1998) 53-73.
	Computable Banach Spaces via Domain Theory (with Philipp Sünderhauf). To appear in Theoretical Computer Science.
	An extension result for continuous valuations (with Mauricio Alvarez-Manilla and Nasser Saheb-Djahromi). Journal of London Mathematical Society (2) 61 (2000) 629-640.
	Domain Theory in stochastic Processes. Proceedings of the Tenth Annual IEEE Symposium on Logic in Computer Science (LICS), (1995), 244-254, IEEE Computer Society.
	Domain Theory in Learning Processes. Electronic Notes in Theoretical Computer Science 1, (1995).
	Domain of computation of a random field in statistical physics. Proceedings of the Second Imperial College, Department of Computing, Theory and Formal Methods Workshop, (1995) Imperial College Press.
	An Algorithm to Estimate the Hausdorff Dimension of Self-Affine Sets (with Jeseph Parry). Electronic notes in Theoretical Computer Science 13, (1998).
	The generalized Riemann Integral on Locally Compact Spaces (with Sara Negri). Toplogy and its Applications. 89 (1998), 121-150.

Bisimulation for Stochastic Processes

	Semi-pullbacks and Bisimulation in Categories of Markov Processes. Mathematical Structures in Computer Science, v.9 n.5, p.523-543, October 1999.
	Bisimulation for Labeled Markov Processes (with Rick Blute and Josee Desharnais and Prakash Panangaden). Twelfth Annual IEEE Symposium on Logic in Computer Science, (1997).
	A Logical Characterization of Bisimulation for Labeled Markov Processes (with Josee Desharnais and Prakash Panangaden). Twelfth Annual IEEE Symposium on Logic in Computer Science, (1998).

Information Systems

	I-Categories as a framework for solving domain equations (with Mike Smyth). Theoretical Computer Science 115, (1993), 77-106.
	Information Categories (with Mike Smyth). Applied Categorical Structures 1, (1993), 197-232.
	Self-duality in Information Categories. Theory and Formal Methods 1993, (1993), 100-114, Springer-Verlag.
	Continuous Information Categories. Lecture Notes in Computer Science 620, (1992), 127-138, Springer-Verlag.

Dynamical Systems

	Equivalence of Degenerate Hopf Bifurcations Nonlinearity 4(3), (1991), 685-695.
	The Stable Classes and the Codimension One Bifurcations of the Planar Replicator System (with E. C. Zeeman) Nonlinearity 5(4), (1992), 921-939.
	The Stability of the Unfolding of the Predator-Prey Model Dynamics and Stability 9(3), (1994), 195-211.
	Bounding the Attractor of an IFS (with D. W. N. Sharp and R. L. While). Information Processing Letters 64(4), (1997), 197-202.