# Revisiting Problem-Solution Co-Evolution in the Context of Team Conceptual Design Activity
## 2 Materials and Methods
### Theoretical Foundations  
Given the introduced diversity of interpretations, there exists a need for developing clear and unambiguous definitions of analysis, synthesis, and evaluation, and their role in design space exploration. In order to tackle this need, the authors synthesised various notions across the literature and conceptualised ASE as three fundamental mechanisms for the exploration of design space, independent of its problem and solution portions. On the fine-grain level of the design process, which is characteristic to the design activity, the instances of such mechanisms appear numerous times, thus continuously changing the state of the product being designed. This transition-based depiction of the design process aligns with the domain-independent descriptive model of design proposed by [PERSON] et al. [59], where the evolution of design space (problem and solution) is represented as a set of states, whereas the act of designing transforms one state into another. By merging the perspective of change in the state of the product being designed and the fine-grain decomposition of the design process into ASE, the team design activity was framed in the form of an ASE state-transition model. In the state-transition model, designing is decomposed into fine-grain transitions that team members perform in order to explore, that is, to change the state of the design space [43]. These transitions imply the creation and assessment of design entities, such as ideas, concepts, and requirements, as well as increasing the understanding of these entities. More precisely, the transitions correspond to the analysis, synthesis, and evaluation of both problem- and solution-related design entities. Consequently, the sequences of transitions represent the evolution of the explored design space; that is, the change of the state of the product being designed, and the state of the design process while teams approach the goal of the design activity (as proposed by [PERSON] et al. [59]). By presuming similar mechanisms for the exploration of both the problem and solution space, the ASE transitions were defined as follows (based on [43]):* Analysis is a state transition resulting in a change in the level of understanding of a particular design entity within the explored design space. Analysis performed in the problem space (problem analysis) clarifies different aspects of the design problem (needs, requirements, constraints, etc.). Analysis performed in the solution space (solution analysis) increases the understanding of the proposed solutions (ideas, concepts, alternatives, etc.). Solution analysis can be performed by determining or learning the behaviour of a solution (how the proposed solution works/behaves) or by clarifying the structure (building shared understanding) of a solution entity. * Synthesis is a state transition resulting in the appearance of a new design entity within the explored design space. Solution synthesis encompasses both the creation of new solutions and the improving, refining, and combining of existing solution entities since the original design entities (the ones being improved/refined/ combined) remain in the solution space, and new derivatives appear. Problem synthesis corresponds to operations aimed at identifying new problem entities and decomposing the given design problem. * Evaluation is a state transition resulting in the assessed appropriacy of a particular design entity within the explored design space and the context of a given design problem. Evaluation of a design entity (in problem or solution space) is performed by addressing a criterion, which is the relevant requirement or constraint entity in the problem space. Problem evaluation is considered as a means of assessing the appropriacy of the problem entities, such as requirements, constraints, or subgoals, whereas solution evaluation corresponds to the assessment of solution entities, such as concept ideas, by focusing on their value and feasibility in the context of the given design problem.