Curriculum Vitae - The University of Texas at Dallas

Section 3: SYNOPSIS OF RESEARCHMy research combines theory and practice. During the past 30+ years I have utilized my PhD research intheory of computation and complexity theory with my systems expertise in industry to develop prototypesbased on fundamental principles. Much of my research during this time was on the design anddevelopment of secure data management systems based on fundamental principles. A synopsis of myresearch follows.After I finished my PhD, starting in 1980, I continued with my research in computability theory andpublished four papers on my thesis work. They are: (i) Cylindrical Decision Problems for SystemFunctions in the Notre Dame Journal of Formal Logic in 1983; System Functions and their DecisionProblems, in Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik. (Mathematical LogicQuarterly) in 1984; The Concept of N-Cylinder and its Application in Zeitschrift fur Mathematische Logikund Grundlagen der Mathematik in 1986; and Reducibility Relationships Between Decision Problems forSystem Functions in Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik in 1987. Untilmy research, there was no generalized framework to study different classes of decision problems. In otherwords, recursion theoretic properties were studied for individual problems such as the halting problem, thederivability problem and the confluence problem. With my framework, we were able to study theindividual problems with the generalized classes. This was a major breakthrough at that time. I develepedcounter-examples for properties that could not be proved. This was achieved by the concept of N-Cylinderwhich I defined. N-Cylinder was an extension of Paul Young’s semi-cylinder. By using the N-Cylinder, Iwas able to show that the general confluence problem was neither recursive nor a cylinder while JohnCleave (my advisor at the University of Bristol) was unable to prove this result back in the early 1970swith the use of Young’s semi-cylinder.Between 1980 and 1983, while at the New Mexico Tech and at the University of Minnesota, I continuedto work on this topic and produced five more journal papers: Representation of One-One Degrees byDecision Problems in the Journal of Computer and Systems Sciences in 1982; Some Elementary ClosureProperties of N-Cylinders in the Notre Dame Journal of Formal Logic in 1983; The Concept of N-Cylinder and its Relationship to Simple Sets in the Notre Dame Journal of Formal Logic in 1983;Representation of One-One Degrees by N-Cylindrical Decision Problems in Zeitschrift furMathematische Logik und Grundlagen der Mathematik in 1988; and System Function Languages inMathematical Logic Quarterly in 1993. Furthermore, there were some questions that John Cleave posed inhis work in the early 1970s which I solved in the early 1980s. Particularly interesting was the followingquestion: could every one-one degree be represented by a particular decision problem? Cleave had shownthat every m-degree could be represented by a decision problem in the early 1970s which was a weakerresult. Cleave believed that the answer to this question would be a major breakthrough as this would showthe existence of decision problems that are Simple. In fact this was the first problem I worked on after myPhD. It was published in the prestigious Journal of Computer and Systems Sciences. This work wouldlater (1989) help me prove that the inference problem was unsolvable, a significant development indatabase security.Between January 1984 and January 1986, I worked at Control Data Corporation as I wanted to get realworld industrial experience working in a product development environment in computer networks anddistributed systems so that I get a feel for how systems really work. During this time I started research insecure dependable distributed systems that would complement my work at Control Data Corporation. Icollaborated with Prof. W. Tsai and his student at the University of Minnesota and together we addressedthe challenging problem of fault tolerance in a binary tree task model. Prior work had focused on a treewith a single child. We felt that binary tree model would be more realistic as tasks usually spawn multipletasks. After several years of work, we published our research in IEEE Transactions on SoftwareEngineering..Due to my increasing interest in secure systems, I joined Honeywell in January 1986 as I felt having aresearch-oriented job would strengthen my research in secure systems. I started working in the challengingarea of secure data management. I was part of a team designing one of the two prominent high assurance7