Overlapping instruction subsets derived from human originated code have previously been shown to dramatically shrink the inductive programming search space, often by many orders of magnitude. Here we extend the instruction subset approach to consider direct instruction-instruction applications (or instruction digrams) as an additional search heuristic for inductive programming. In this study we analyse the frequency distribution of instruction digrams in a large sample of open source code. This indicates that the instruction digram distribution is highly skewed with over 93% of possible instruction digrams not represnted in the code sample. We demonstrate that instruction digrams can be used to constrain instruction selection during search, further reducing size of the the search space, in some cases by several orders of magnitude. This significantly increases the size of programs that can be generated using search based inductive programming techniques. We discuss the results and provide some suggestions for further work.

SEQUITUR is an algorithm that infers a hierarchical structure from a sequence of discrete symbols by replacing repeated phrases with a grammatical rule that generates the phrase, and continuing this process recursively. The result is a hierarchical representation of the original sequence, which offers insights into its lexical structure. The algorithm is driven by two constraints that reduce the size of the grammar, and produce structure as a by-product. SEQUITUR breaks new ground by operating incrementally. Moreover, the method's simple structure permits a proof that it operates in space and time that is linear in the size of the input. Our implementation can process 50,000 symbols per second and has been applied to an extensive range of real world sequences.