Solving algebra problems (APs) continues to attract significant research interest as evidenced by the large number of algorithms and theories proposed over the past decade. Despite these important research contributions, however, the body of work remains incomplete in terms of theoretical justification and scope. The current contribution intends to fill the gap by developing a review framework that aims to lay a theoretical base, create an evaluation scheme, and extend the scope of the investigation. This paper first develops the State Transform Theory (STT), which emphasizes that the problem-solving algorithms are structured according to states and transforms unlike the understanding that underlies traditional surveys which merely emphasize the progress of transforms. The STT, thus, lays the theoretical basis for a new framework for reviewing algorithms. This new construct accommodates the relation-centric algorithms for solving both word and diagrammatic algebra problems. The latter not only highlights the necessity of introducing new states but also allows revelation of contributions of individual algorithms obscured in prior reviews without this approach.

翻译：代数问题（APs）的求解在过去十年间吸引了大量研究关注，众多算法与理论相继提出即为明证。然而，尽管已有这些重要的研究成果，现有工作在理论依据与研究范围方面仍存在不足。本文旨在通过构建一个综述框架来填补这一空白，该框架致力于奠定理论基础、建立评估体系并拓展研究范围。本文首先提出了状态转换理论（STT），该理论强调问题求解算法是依据状态与转换而构建的，这与传统综述仅强调转换过程的理解有所不同。因此，STT为算法综述的新框架奠定了理论基础。这一新架构能够涵盖面向文字与图示代数问题的关系核心算法。后者不仅凸显了引入新状态的必要性，还得以揭示先前综述中因缺乏此方法而被掩盖的各个算法的贡献。