Software product lines (SPLs) facilitate reuse and customization in software development by genuinely addressing the concept of variability. Product Line Calculus of Communicating Systems (PL-CCS) is a process calculus for behavioral modeling of SPLs, in which variability can be explicitly modeled by a binary variant operator. In this paper, we study different notions of behavioral equivalence for PL-CCS, based on Park and Milner's strong bisimilarity. These notions enable reasoning about the behavior of SPLs at different levels of abstraction. We study the compositionality property of these notions and the mutual relationship among them. We further show how the strengths of these notions can be consolidated in an equational reasoning method. Finally, we designate the notions of behavioral equivalence that are characterized by the property specification language for PL-CCS, called multi-valued modal μ-calculus. 
Product line process theory