Minimal Synthesis of String To String Functions From Examples

TL;DR

This paper addresses the challenge of synthesizing minimal string-to-string transformations from examples using finite automata, proving NP-completeness and proposing an SMT-based algorithm for practical solution.

Contribution

It introduces the problem of minimal DFA synthesis from examples with constraints, proves its NP-completeness, and provides an SMT-based algorithm for finding solutions.

Findings

NP-hardness of minimal DFA synthesis from examples

Proposed SMT-based algorithm for practical minimal DFA synthesis

Evaluation shows the algorithm's effectiveness in real-world scenarios

Abstract

We study the problem of synthesizing string to string transformations from a set of input/output examples. The transformations we consider are expressed using deterministic finite automata (DFA) that read pairs of letters, one letter from the input and one from the output. The DFA corresponding to these transformations have additional constraints, ensuring that each input string is mapped to exactly one output string. We suggest that, given a set of input/output examples, the smallest DFA consistent with the examples is a good candidate for the transformation the user was expecting. We therefore study the problem of, given a set of examples, finding a minimal DFA consistent with the examples and satisfying the functionality and totality constraints mentioned above. We prove that, in general, this problem (the corresponding decision problem) is NP-complete. This is unlike the standard DFA minimization problem which can be solved in polynomial time. We provide several NP-hardness proofs that show the hardness of multiple (independent) variants of the problem. Finally, we propose an algorithm for finding the minimal DFA consistent with input/output examples, that uses a reduction to SMT solvers. We implemented the algorithm, and used it to evaluate the likelihood that the minimal DFA indeed corresponds to the DFA expected by the user.