Jiazhen Cai

Geometric constraint solver

Abstract The paper reports on the development of a 2D geometric constraint solver. The solver is a major component of a new generation of cad systems based on a high-level geometry representation. The solver uses a graph-reduction directed algebraic approach, and achieves interactive speed. The paper describes the architecture of the solver and its basic capabilities. Then, it discusses in detail how to extend the scope of the solver, with particular emphasis on the theoretical and human factors involved in finding a solution, in an exponentially large search space, so that the solution is appropriate to the application, and so that the way of finding it is intuitive for an untrained user.

Program derivation by fixed point computation

Abstract This paper develops a transformational paradigm by which nonnumerical algorithms are treated as fixed point computations derived from very high level problem specifications. We begin by presenting an abstract functional problem specification language SQ+, which is shown to express any partial recursive function in a fixed point normal form. Next, we give a nondeterministic iterative schema that in the case of finite iteration generalizes the “chaotic iteration” of Cousot and Cousot for computing fixed points of monotone functions efficiently. New techniques are discussed for recomputing fixed points of distributive functions efficiently. Numerous examples illustrate how these techniques for computing and recomputing fixed points can be incorporated within a transformational programming methodology to facilitate the design and verification of nonnumerical algorithms.

An O(m log n) -time algorithm for the maximal planar subgraph problem

Based on a new version of the Hopcroft and Tarjan planarity testing algorithm, this paper develops an

Binding performance at language design time

O(m\log n)

Towards increased productivity of algorithm implementation

-time algorithm to find a maximal planar subgraph.

Using multiset discrimination to solve language processing problems without hashing

An important research goal in software engineering and programming languages is the development of principles underlying the specification of computable problems, the <italic>translation of these problems into efficient and correct</italic> programs, and the performance analysis of these programs. This paper uncovers some of these principles, which are used to design a problem specification language L<subscrpt>1</subscrpt> restricted to problems that can be compiled automatically into programs whose worst case asymptotic time and space complexities are linear in the input/output space. Any problem expressible in L<subscrpt>1</subscrpt> can be compiled into a linear cost program. A compiler for L<subscrpt>1</subscrpt> has been implemented in the RAPTS transformational programming system.

More efficient bottom-up multi-pattern matching in trees

This paper reports experimental results that support the feasibility of a new transformational approach developed by the authors for implementing complex algorithms correctly and efficiently. The class of algorithms amenable to our methods includes nonnumerical graph algorithms. Experiments were performed to measure how this approach affects productivity (in terms of the number of source lines in the implementation divided by manual programming time) and running times. Comparative benchmarks showed that productivity can be increased over a conventional ad hoc approach by factors ranging from 5.1 to 9.9 Preliminary results also showed that the running time of C code produced by this new approach can be as fast as 1.5 times that of tightly coded high quality Fortran.