Thomas G. Szymanski

A fast algorithm for computing longest common subsequences

Previously published algorithms for finding the longest common subsequence of two sequences of length n have had a best-case running time of O(n2). An algorithm for this problem is presented which has a running time of O((r + n) log n), where r is the total number of ordered pairs of positions at which the two sequences match. Thus in the worst case the algorithm has a running time of O(n2 log n). However, for those applications where most positions of one sequence match relatively few positions in the other sequence, a running time of O(n log n) can be expected.

Data compression via textual substitution

A general model for data compression which includes most data compression systems in the fiterature as special cases is presented. Macro schemes are based on the principle of finding redundant strings or patterns and replacing them by pointers to a common copy. Different varieties of macro schemes may be defmed by specifying the meaning of a pointer; that is, a pointer may indicate a substring of the compressed string, a substring of the original string, or a substring of some other string such as an external dictionary. Other varieties of macro schemes may be defined by restricting the type of overlapping or recursion that may be used. Trade-offs between different varieties of macro schemes, exact lower bounds on the amount of compression obtainable, and the complexity of encoding and decoding are discussed, as well as how the work of other authors relates to this model.

Inferring a Tree from Lowest Common Ancestors with an Application to the Optimization of Relational Expressions

We present an algorithm for constructing a tree to satisfy a set of lineage constraints on common ancestors. We then apply this algorithm to synthesize a relational algebra expression from a simple tableau, a problem arising in the theory of relational databases.

On the equivalence, containment, and covering problems for the regular and context-free languages

We consider the complexity of the equivalence and containment problems for regular expressions and context-free grammars, concentrating on the relationship between complexity and various language properties. Finiteness and boundedness of languages are shown to play important roles in the complexity of these problems. An encoding into grammars of Turing machine computations exponential in the size of the grammar is used to prove several exponential lower bounds. These lower bounds include exponential time for testing equivalence of grammars generating finite sets, and exponential space for testing equivalence of non-self-embedding grammars. Several problems which might be complex because of this encoding are shown to simplify for linear grammars. Other problems considered include grammatical covering and structural equivalence for right-linear, linear, and arbitrary grammars.

Computing optimal clock schedules

The author considers the problem of optimizing the parameters of a multiphase clock for a circuit containing both edge-triggered flip-flops and level-sensitive latches. He demonstrates that recently proposed linear programming (LP) approaches to this problem require excessive computation time. An alternative method is proposed in which LP constraints are generated selectively, thus allowing fast solution. Various formulations of short path constraints are discussed, as are experimental results for large circuits.<<ETX>>

Verifying clock schedules

Timing verification and optimization have been formulated as mathematical programming problems. The computational aspects of using such a formulation for verifying clock schedules are considered. The formulation can have multiple solutions, and these extraneous solutions can cause previously published algorithms to produce incorrect or misleading results. The conditions under which multiple solutions exist are characterized, and it is shown that even when the solution is unique, the running times of these previous algorithms can be unbounded. By contrast, a simple polynomial time algorithm for clock schedule verification is exhibited. The algorithm was implemented and used to check the timing of all the circuits in the ISCAS-89 benchmark suite. Observed running times are linear in circuit size and quite practical. >

Goalie: A Space Efficient System for VLSI Artwork Analysis

Advances in VLSI have resulted in more and more complex circuitry, fueling the need for programs that analyze IC mask artwork. This article describes Goalie, an artwork analysis system, by explaining the algorithms used to support circuit extraction, Boolean geometric operations, connectivity analysis, capacitance measurement and design checking. Tests on several systems have shown that Goalie runs at least as fast as algorithms currently in use, but it requires less main memory, so large layouts can be handled on small computers, or even on personal workstations.

Space Efficient Algorithms for VLSI Artwork Analysis

We present algorithms for performing connectivity analysis, transistor identification, and boolean geometric operations with region numbering. Previous methods all require O(n) space where n is the number of edges in the circuit artwork; our method takes only O(√n) space and can therefore handle circuits of any foreseeable size. Our algorithms are based on traditional scanline techniques in such a way that any implementation of our method will be at least as fast, as well as more compact. Statistics on one such implementation are presented.

Assembling code for machines with span-dependent instructions

Many modern computers contain instructions whose lengths depend on the distance from a given instance of such an instruction to the operand of that instruction. This paper considers the problem of minimizing the lengths of programs for such machines. An efficient solution is presented for the case in which the operand of every such “span-dependent” instruction is either a label or an assembly-time expression of a certain restricted form. If this restriction is relaxed by allowing these operands to be more general assembly-time expressions, then the problem is shown to be NP-complete.

Non-Canonical Extensions of Bottom-Up Parsing Techniques

A bottom-up parsing technique which can make non-leftmost possible reductions in sentential forms is said to be non-canonical. Nearly every existing parsing technique can be extended to a non-canonical method which operates on larger classes of grammars and languages than the original technique. Moreover, the resulting parsers run in time linearly proportional to the length of their input strings. Several such extensions are defined and analyzed from the points of view of both power and decidability. The results are presented in terms of a general bottom-up parsing model which yields a common decision procedure for testing membership in many of the existing and extended classes.