This paper presents the context-updates synthesis component of Chisel-a tool that synthesizes a program slicer directly from a given algebraic specification of a programming language operational semantics. (By context-updates we understand programming language constructs such as goto instructions or function calls.) The context-updates synthesis follows two directions: an overapproximating phase that extracts a set of potential context-update constructs and an underapproximating phase that refines the results of the first step by testing the behaviour of the context-updates constructs produced at the previous phase. We use two experimental semantics that cover two types of language paradigms: high-level imperative and low-level assembly languages and we conduct the tests on standard benchmarks used in avionics.