Minimal Synthesis of String To String Functions From Examples

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.Comment: SYNT 201

Machine learning for emergent middleware

Highly dynamic and heterogeneous distributed systems are challenging today's middleware technologies. Existing middleware paradigms are unable to deliver on their most central promise, which is offering interoperability. In this paper, we argue for the need to dynamically synthesise distributed system infrastructures according to the current operating environment, thereby generating "Emergent Middleware'' to mediate interactions among heterogeneous networked systems that interact in an ad hoc way. The paper outlines the overall architecture of Enablers underlying Emergent Middleware, and in particular focuses on the key role of learning in supporting such a process, spanning statistical learning to infer the semantics of networked system functions and automata learning to extract the related behaviours of networked systems

Learning Moore Machines from Input-Output Traces

The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning theory and practice. In this paper we study this problem for finite state machines with inputs and outputs, and in particular for Moore machines. We develop three algorithms for solving this problem: (1) the PTAP algorithm, which transforms a set of input-output traces into an incomplete Moore machine and then completes the machine with self-loops; (2) the PRPNI algorithm, which uses the well-known RPNI algorithm for automata learning to learn a product of automata encoding a Moore machine; and (3) the MooreMI algorithm, which directly learns a Moore machine using PTAP extended with state merging. We prove that MooreMI has the fundamental identification in the limit property. We also compare the algorithms experimentally in terms of the size of the learned machine and several notions of accuracy, introduced in this paper. Finally, we compare with OSTIA, an algorithm that learns a more general class of transducers, and find that OSTIA generally does not learn a Moore machine, even when fed with a characteristic sample

Learning deterministic probabilistic automata from a model checking perspective

Probabilistic automata models play an important role in the formal design and analysis of hard- and software systems. In this area of applications, one is often interested in formal model-checking procedures for verifying critical system properties. Since adequate system models are often difficult to design manually, we are interested in learning models from observed system behaviors. To this end we adopt techniques for learning finite probabilistic automata, notably the Alergia algorithm. In this paper we show how to extend the basic algorithm to also learn automata models for both reactive and timed systems. A key question of our investigation is to what extent one can expect a learned model to be a good approximation for the kind of probabilistic properties one wants to verify by model checking. We establish theoretical convergence properties for the learning algorithm as well as for probability estimates of system properties expressed in linear time temporal logic and linear continuous stochastic logic. We empirically compare the learning algorithm with statistical model checking and demonstrate the feasibility of the approach for practical system verification

Generating Models of Infinite-State Communication Protocols Using Regular Inference with Abstraction

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State identification problems for timed automata

Abstract. A well-established theory exists for testing finite state machines. One fundamental class of problems handled by this theory is state identification: we are given a machine with known state space and transition relation, but unknown initial state, and we are asked to find tests which identify the initial or final state of the machine. In this paper, we study state identification in the context of timed automata which contrary to, say, Mealy or Moore machines, is a suitable model for real-time systems. We are interested in digital-clock tests which have a finite clock precision and are thus implementable. We develop a general technique, based on time-abstracting bisimulation, which reduces the problem to the case of non-deterministic finite-state Mealy machines. We illustrate our technique on a toy example.

Learning meets Verification

Abstract. In this paper, we give an overview on some algorithms for learning automata. Starting with Biermann’s and Angluin’s algorithms, we describe some of the extensions catering for specialized or richer classes of automata. Furthermore, we survey their recent application to verification problems.