Enumerating Building Block Semantics in Genetic Programming

This report provides a collection of definitions for the semantics of sub-trees and contexts as manipulated by standard sub-tree crossover in genetic programming (GP). These definitions allow us to completely and compactly describe the exact semantics of the components manipulated by sub-tree crossover, and the semantic results of those interactions. Sub- sequent work shows how these definitions can be used to collect valuable data about the available diversity in a GP population and the opportunities available to sub-tree crossover

Semantic Building Blocks in Genetic Programming

In this paper we present a new mechanism for studying the impact of subtree crossover in terms of semantic building blocks. This approach allows us to completely and compactly describe the semantic action of crossover, and provide insight into what does (or doesn’t) make crossover effective. Our results make it clear that a very high proportion of crossover events (typically over 75% in our experiments) are guaranteed to perform no immediately useful search in the semantic space. Our findings also indicate a strong correlation between lack of progress and high proportions of fixed contexts. These results then suggest several new, theoretically grounded, research areas

Algorithms for Extended Alpha-Equivalence and Complexity

Equality of expressions in lambda-calculi, higher-order programming languages, higher-order programming calculi and process calculi is defined as alpha-equivalence. Permutability of bindings in let-constructs and structural congruence axioms extend alpha-equivalence. We analyse these extended alpha-equivalences and show that there are calculi with polynomial time algorithms, that a multiple-binding “let ” may make alpha-equivalence as hard as finding graph-isomorphisms, and that the replication operator in the pi-calculus may lead to an EXPSPACE-hard alpha-equivalence problem

Limit Cycle Displacement Model of Circadian Rhythms

A mathematical model has been examined that attempts to mimic the effects of changes in environmental conditions on circadian rhythms. The basis of the model claims that for a given set of environmental conditions (e.g., light, temperature and chemical concentrations) there exists a limit cycle that has a given position. When an environmental treatment is applied that is different from the control conditions, the position of the new limit cycle changes and the oscillating parameters of the circadian system are now attracted toward this newly positioned limit cycle. If conditions are subsequently returned back to control levels, the control limit cycle again takes effect and the displaced parameters are attracted back to the postion of control limit cycle. The model provides a description of what happens as a result of a pulse of new environmental conditions as well as what happens while the new conditions are in effect. Actual results involving entrainment, phase-release, and pulse experiments are compared to modeled results and a positive correlation is seen. Equations in closed form have been developed from the model that describe release-assay curves and phase response curves (including the transition between type 1 and type 0 behavior). Presumably a change in environmental conditions changes several aspects of a circadian rhythm limit cycle, but this work suggests that most of the features of a circadian rhythm experiment can be qualitatively mimicked by simply shifting the position of the limit cycle relative to new environmental conditions

Computational Soundness of a Call by Name Calculus of Recursively-scoped Records

The paper presents a calculus of recursively-scoped records: a two-level calculus with a traditional call-byname λ-calculus at a lower level and unordered collections of labeled λ-calculus terms at a higher level. Terms in records may reference each other, possibly in a mutually recursive manner, by means of labels. We define two relations: a rewriting relation that models program transformations and an evaluation relation that defines a small-step operational semantics of records. Both relations follow a call-by-name strategy. We use a special symbol called a black hole to model cyclic dependencies that lead to infinite substitution. Computational soundness is a property of a calculus that connects the rewriting relation and the evaluation relation: it states that any sequence of rewriting steps (in either direction) preserves the meaning of a record as defined by the evaluation relation. The computational soundness property implies that any program transformation that can be represented as a sequence of forward and backward rewriting steps preserves the meaning of a record as defined by the small step operational semantics. In this paper we describe the computational soundness framework and prove computational soundness of the calculus. The proof is based on a novel inductive context-based argument for meaning preservation of substituting one component into another

A finite simulation method in a non-deterministic call-by-need calculus with letrec, constructors and case

The paper proposes a variation of simulation for checking and proving contextual equivalence in a non-deterministic call-by-need lambda-calculus with constructors, case, seq, and a letrec with cyclic dependencies. It also proposes a novel method to prove its correctness. The calculus' semantics is based on a small-step rewrite semantics and on may-convergence. The cyclic nature of letrec bindings, as well as non-determinism, makes known approaches to prove that simulation implies contextual equivalence, such as Howe's proof technique, inapplicable in this setting. The basic technique for the simulation as well as the correctness proof is called pre-evaluation, which computes a set of answers for every closed expression. If simulation succeeds in finite computation depth, then it is guaranteed to show contextual preorder of expressions