I wish to model the following common construction in code via a finite state automaton for the purposes of static analysis:

s = <string matching regex R1>
t = s.replace(<regex R2>, <string matching regex R3>)
# What is the set of possible strings of t?

More formally, given DFAs $R_1$, $R_2$, and $R_3$, I want to find some automaton $R_o$ that is the result of replacing substrings of $R_1$ that are accepted by $R_2$ by some string that is accepted by $R_3$.

Unfortunately, while the literature seems to discuss this, I am unable to pin down a precise implementation of this operation. In addition, I am having trouble even defining the set of strings that $R_o$ should accept. Does there exist an algorithm to solve this problem? Is it even solvable in general?


1 Answer 1


Depending on the exact semantics of the replace operation (regarding multiple matches, overlapping matches, etc.), it can likely be modelled as a finite-state transducer. The set of possible values of s can be modelled as a regular language. It is known that the application of a finite-state transducer to a regular language gives you another regular language, and there are standard algorithms for computing it, using the product construction.


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