Computational analysis of data produced in deep sequencing experiments is challenging due to large data volumes and requirements for flexible analysis approaches. Here we present a mathematical formalism based on set algebra for frequently performed operations in deep sequencing data analysis to facilitate translation of biomedical research questions to language amenable for computational analysis. With the help of this formalism we implemented Genomic Region Operation Kit (GROK), which supports various deep sequencing related operations such as preprocessing, filtering, file conversion and sample comparison. GROK provides high level interfaces for R, Python, Lua and command line, as well as an extension C++ API. It supports major genomic file formats and allows storing custom genomic regions in efficient data structures such as red-black trees and SQL databases. To demonstrate the utility of GROK we have characterized the roles of two major transcription factors in prostate cancer using data from ten deep sequencing experiments. GROK is freely available with a user guide from http://csbi.ltdk.helsinki.fi/grok/.