Letter-to-letter transducers are a standard formalism for modeling reactive systems. Often, two transducers that model similar systems differ locally from one another, by behaving similarly, up to permutations of the input and output letters within "rounds". In this work, we introduce and study notions of simulation by rounds and equivalence by rounds of transducers. In our setting, words are partitioned to consecutive subwords of a fixed length $k$, called rounds. Then, a transducer $\mathcal{T}_1$ is $k$-round simulated by transducer $\mathcal{T}_2$ if, intuitively, for every input word $x$, we can permute the letters within each round in $x$, such that the output of $\mathcal{T}_2$ on the permuted word is itself a permutation of the output of $\mathcal{T}_1$ on $x$. Finally, two transducers are $k$-round equivalent if they simulate each other. We solve two main decision problems, namely whether $\mathcal{T}_2$ $k$-round simulates $\mathcal{T}_1$ (1) when $k$ is given as input, and (2) for an existentially quantified $k$. We demonstrate the usefulness of the definitions by applying them to process symmetry: a setting in which a permutation in the identities of processes in a multi-process system naturally gives rise to two transducers, whose $k$-round equivalence corresponds to stability against such permutations.

We present TackleTest, an open-source tool for automatic generation of unit-level test cases for Java applications. TackleTest builds on top of two well-known test-generation tools, EvoSuite and Randoop, by adding a new combinatorial-testing-based approach for computing coverage goals that comprehensively exercises different parameter type combinations of the methods under test, at configurable interaction levels. We describe the tool architecture, the main tool components, and the combinatorial type-based testing technique. TackleTest was developed in the context of application modernization at IBM, but it is also applicable as a general-purpose test-generation tool. We have evaluated TackleTest on several IBM-internal enterprise applications as well as on a subset of the SF110 benchmark, and share our findings and lessons learned. Overall, TackleTest implements a new and complementary way of computing coverage goals for unit testing via a novel white-box application of combinatorial testing.