Show HN: State Algebra, new algebraic framework for logic, an alternative to BDD (arxiv.org)

Dmitry Lesnik’s arXiv paper introduces State Algebra, a new algebraic framework for representing and manipulating propositional logic that the author positions as an alternative to BDD-style representations. The framework organizes logical objects in a three-tier hierarchy—Set, Coordinate, and Row Decomposition—anchoring each layer in standard semantics while enabling manipulation via an algebraic “engine.” States are encoded as vectors and reduced algebraically; the default reduction is not guaranteed canonical, but a unique canonical form can be enforced by fixing a variable order during reduction. That design intentionally trades guaranteed canonicity for representational flexibility, which the paper argues can produce more compact encodings for certain problem classes. The framework also cleanly expresses both search-based procedures and knowledge-compilation style algorithms, and the paper sketches straightforward extensions to probabilistic logic and Weighted Model Counting. For the AI/ML community, State Algebra matters because it provides a different point in the design space from BDDs and other canonical forms: by relaxing canonicity you may get smaller or faster representations for specific workloads, while retaining the option to force canonicity when needed (via variable ordering). Its compatibility with search, knowledge compilation, and WMC suggests immediate relevance to SAT solving, probabilistic inference, and model counting tasks common in probabilistic programming and ML pipelines. If implementations realize the promised compactness and algebraic manipulability, State Algebra could enable new hybrid compilation/search algorithms and more efficient probabilistic inference primitives.