Certified Symbolic Finite Transducers: Formalization and Applications to String Analysis

Finite Automata (FAs) are fundamental components in the domains of programming languages. For instance, regular expressions, which are pivotal in languages such as JavaScript and Python, are frequently implemented using FAs. Finite Transducers (FTs) extend the capabilities of FAs by enabling the transformation of input strings into output strings, thereby providing a more expressive framework for operations that encompass both recognition and transformation. Despite the various formalizations of FAs in proof assistants such as Coq and Isabelle/HOL, these formalizations often fall short in terms of applicability to real-world scenarios. A more pragmatic approach involves the formalization of symbolic FAs and FTs, where transition labels are symbolic and potentially infinite. While the formalization of symbolic FAs has been explored in the work of CertiStr, the formalization of symbolic FTs in interactive proof assistants remains largely unexplored due to the increased complexity challenges. In this paper, we aim to formalize symbolic FTs within the Isabelle/HOL framework. This formalization is refinement-based and is designed to be extensible with various symbolic representations of transition labels. To assess its performance, we applied the formalized symbolic FTs to an SMT string solver for modeling replacement operations. The experimental results indicate that the formalized symbolic transducer can efficiently and effectively solve string constraints with replacement operations.