On Unfolding Completeness for Rewriting Logic Theories

Many transformation systems for program optimization, program synthesis, and program specialization are based on fold/unfold transformations. In this paper, we investigate the semantic properties of a narrowing-based unfolding transformation that is useful to transform rewriting logic theories. We also present a transformation methodology that is able to determine whether an unfolding transformation step would cause incompleteness and avoid this problem by completing the transformed rewrite theory with suitable extra rules. More precisely, our methodology identifies the sources of incompleteness and derives a set of rules that are added to the transformed rewrite theory in order to preserve the semantics of the original theory.Alpuente Frasnedo, M.; Baggi, M.; Ballis, D.; Falaschi, M. (2010). On Unfolding Completeness for Rewriting Logic Theories. http://hdl.handle.net/10251/863

Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis

Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing and energy consumption, and the automatic synthesis of systems from specifications. The major challenges include environment modeling, incompleteness in specifications, and the complexity of underlying decision problems. This position paper proposes sciduction, an approach to tackle these challenges by integrating inductive inference, deductive reasoning, and structure hypotheses. Deductive reasoning, which leads from general rules or concepts to conclusions about specific problem instances, includes techniques such as logical inference and constraint solving. Inductive inference, which generalizes from specific instances to yield a concept, includes algorithmic learning from examples. Structure hypotheses are used to define the class of artifacts, such as invariants or program fragments, generated during verification or synthesis. Sciduction constrains inductive and deductive reasoning using structure hypotheses, and actively combines inductive and deductive reasoning: for instance, deductive techniques generate examples for learning, and inductive reasoning is used to guide the deductive engines. We illustrate this approach with three applications: (i) timing analysis of software; (ii) synthesis of loop-free programs, and (iii) controller synthesis for hybrid systems. Some future applications are also discussed

Input Synthesis for Sampled Data Systems by Program Logic

Inspired by a concrete industry problem we consider the input synthesis problem for hybrid systems: given a hybrid system that is subject to input from outside (also called disturbance or noise), find an input sequence that steers the system to the desired postcondition. In this paper we focus on sampled data systems--systems in which a digital controller interrupts a physical plant in a periodic manner, a class commonly known in control theory--and furthermore assume that a controller is given in the form of an imperative program. We develop a structural approach to input synthesis that features forward and backward reasoning in program logic for the purpose of reducing a search space. Although the examples we cover are limited both in size and in structure, experiments with a prototype implementation suggest potential of our program logic based approach.Comment: In Proceedings HAS 2014, arXiv:1501.0540

Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs

Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating reachability probabilities. Based on the existing works that stretch across different communities (formal verification, control theory, etc.), we offer a unifying account. In particular, we emphasize the role of order-theoretic fixed points---a classic topic in computer science---in the analysis of probabilistic programs. This leads us to two new martingale-based techniques, too. We give rigorous proofs for their soundness and completeness. We also make an experimental comparison using our implementation of template-based synthesis algorithms for those martingales

Mixin Composition Synthesis based on Intersection Types

We present a method for synthesizing compositions of mixins using type inhabitation in intersection types. First, recursively defined classes and mixins, which are functions over classes, are expressed as terms in a lambda calculus with records. Intersection types with records and record-merge are used to assign meaningful types to these terms without resorting to recursive types. Second, typed terms are translated to a repository of typed combinators. We show a relation between record types with record-merge and intersection types with constructors. This relation is used to prove soundness and partial completeness of the translation with respect to mixin composition synthesis. Furthermore, we demonstrate how a translated repository and goal type can be used as input to an existing framework for composition synthesis in bounded combinatory logic via type inhabitation. The computed result is a class typed by the goal type and generated by a mixin composition applied to an existing class