Harry B. Hunt

NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs

We present NC-approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner. Our approximation schemes exhibit the same time versus performance trade-off as the best known approximation schemes for planar graphs. We also define the concept of ?-precision unit disk graphs and show that for such graphs the approximation schemes have a better time versus performance trade-off than the approximation schemes for arbitrary unit disk graphs. Moreover, compared to unit disk graphs, we show that for ?-precision unit disk graphs many more graph problems have efficient approximation schemes.Our NC-approximation schemes can also be extended to obtain efficient NC-approximation schemes for several PSPACE-hard problems on unit disk graphs specified using a restricted version of the hierarchical specification language of Bentley, Ottmann, and Widmayer. The approximation schemes for hierarchically specified unit disk graphs presented in this paper are among the first approximation schemes in the literature for natural PSPACE-hard optimization problems.

On computing signal probability and detection probability of stuck-at faults

Algorithms for the following two problems are presented: (1) computing detection probability of stuck-at faults (CDP), and (2) computing signal probability (CSP). These problems arise in the context of random testing, pseudorandom testing, and testability analysis of combinational circuits. The algorithm for CDP combines the notion of supergates and a refinement of th algorithm for CDP presented in the work of S. Chakravarty and H.B. Hunt, III (1986). The algorithm for CDP can be used to compute the exact value of detection probability of multiple stuck-at faults in circuits with multiple outputs. Single-input, single-output pseudo gates are inserted to model stuck-at faults and derive an equivalent single-output circuit. CDP is thus reduced to the problem of computing the probability distribution of the output over the set of four logic values (0, 1d, d). The algorithm for CDP uses an efficient enumeration algorithm. The authors show how the enumeration algorithm can be used to refine the algorithm for CSP. >

On the complexity of relational problems for finite state processes

We study the complexity of the following three relational problems: Let ∼ be a binary relation on finite state processes; let p0 be a fixed finite state process; and let π be a nontrivial predicate on finite state processes such that x and y are weakly bisimilar implies π(x) = π(y). (i) P1: Determine for processes p and q, if p ∼ q; (ii) P2 Determine for process p, if p ∼ p0; and (iii) P3: Determine for process p, if π(p) = true. We study the complexities of these problems, when processes are represented by sequential transition systems and by parallel composition of transition systems (with and without hiding). A number of results are obtained for both representations.

The complexity of very simple Boolean formulas with applications

The concepts of

The complexity of approximating pspace-complete problems for hierarchical specifications

\textbf{SAT}

Nonlinear algebra and optimization on rings are “hard”

-hardness and

Efficient approximation algorithms for domatic partition and on-line coloring of circular arc graphs

\textbf{SAT}

Strongly-local reductions and the complexity/efficient approximability of algebra and optimization on abstract algebraic structures

-completeness modulo npolylogn time and linear size reducibility, denoted by

On computing reliability-measures of Boolean circuits

\textbf{SAT}

Matrix multiplication for finite algebraic systems

-hard (npolylogn, n) and