Journal of Data Processing Davide Morelli, Antonio Cisternino 15 2 2025 https://doi.org/10.6025/jdp/2025/15/2/59-66 https://www.dline.info/jdp/fulltext/v15n2/jdpv15n2_2.pdf This paper presents a compositional and algebraic model for characterizing software and hardware based on their resource usage, with a focus on energy consumption and completion time. Recognising the limitations of instruction-level profiling and the nondeterminism introduced by modern system complexities, the authors propose a black-box approach that measures the overall resource usage of programs without requiring source code access. By treating programs as combinations of computational patterns, the model uses synthetic benchmarks as building blocks to represent programs in terms of their resource behavior. The authors introduce a linear algebra framework where resource usage data is captured in matrices, enabling decomposition of programs into benchmark-based components. The model defines three conceptual spaces—measurement space, splitup space, and benchmark space—to analyze program behavior, system characteristics, and resource efficiency. This enables comparison of software across systems and identification of unknown computational patterns. Experimental results on a desktop system demonstrate how the model captures the growing dominance of memory operations in mergesort as input size increases. The approach offers a scalable, source-independent method for profiling and predicting energy and performance behavior across heterogeneous environments. Future work will explore applications in cloud computing, virtual machines, and heterogeneous architectures for real-time resource forecasting.