Lambda-upsilon-omega: An assistant algorithms analyzer. (English) Zbl 0681.68064

Flajolet, Philippe; Salvy, Bruno; Zimmermann, Paul

Applied algebra, algebraic algorithms and error-correcting codes, Proc. 6th Int. Conference, AAECC-6, Rome/Italy 1988, Lect. Notes Comput. Sci. 357, 201-212 (1989).

Summary: [For the entire collection see Zbl 0671.00023.]
Lambda-Upsilon-Omega, \(\Lambda_{\Upsilon}\Omega\), is a system designed to perform automatic analysis of well-defined classes of algorithms operating over “decomposable” data structures. It consists of an ‘Algebraic Analyzer’ System that compiles algorithms specifications into generating functions of average costs, and an ‘Analytic Analyzer’ System that extracts asymptotic informations on coefficients of generating functions. The algebraic part relies on recent methodologies in combinatorial analysis based on systematic correspondences between structural type definitions and counting generating functions. The analytic part makes use of partly classical and partly new correspondences between singularities of analytic functions and the growth of their Taylor coefficients. The current version \(\Lambda_{\Upsilon}\Omega_ 0\) of \(\Lambda_{\Upsilon}\Omega\) implements as basic data types, term trees as encountered in symbolic algebra systems. The analytic analyzer can treat large classes of functions with explicit expressions. In this way, \(\Lambda_{\Upsilon}\Omega_ 0\) can generate in the current stage about a dozen non-trivial average case analyzes of algorithms like: formal differentiation, some algebraic simplification and matching algorithms. Its analytic analyzer can determine asymptotic expansions for large classes of generating functions arising in the analysis of algorithms. The outline of a design for a full system is also discussed here. The long term goal is to include a fairly rich set of data structuring mechanisms including some general recursive type definitions, and have the analytic analyzer treat wide classes of functional equations as may be encountered in combinatorial analysis and the analysis of algorithms.

MSC:

68Q25	Analysis of algorithms and problem complexity
68W30	Symbolic computation and algebraic computation
05A15	Exact enumeration problems, generating functions
68P05	Data structures
68Q60	Specification and verification (program logics, model checking, etc.)

Keywords:

algorithms analyzer; automatic analysis; data structures; Algebraic Analyzer; generating functions; combinatorial analysis; data types; term trees; average case analyzes of algorithms; analysis of algorithms

Citations:

Zbl 0671.00023