Synthesizing Modular Invariants for Synchronous Code

In this paper, we explore different techniques to synthesize modular invariants for synchronous code encoded as Horn clauses. Modular invariants are a set of formulas that characterizes the validity of predicates. They are very useful for different aspects of analysis, synthesis, testing and program transformation. We describe two techniques to generate modular invariants for code written in the synchronous dataflow language Lustre. The first technique directly encodes the synchronous code in a modular fashion. While in the second technique, we synthesize modular invariants starting from a monolithic invariant. Both techniques, take advantage of analysis techniques based on property-directed reachability. We also describe a technique to minimize the synthesized invariants.Comment: In Proceedings HCVS 2014, arXiv:1412.082

Generating Non-Linear Interpolants by Semidefinite Programming

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Comment: 22 pages, 4 figure

Monitoring-Oriented Programming: A Tool-Supported Methodology for Higher Quality Object-Oriented Software

This paper presents a tool-supported methodological paradigm for object-oriented software development, called monitoring-oriented programming and abbreviated MOP, in which runtime monitoring is a basic software design principle. The general idea underlying MOP is that software developers insert specifications in their code via annotations. Actual monitoring code is automatically synthesized from these annotations before compilation and integrated at appropriate places in the program, according to user-defined configuration attributes. This way, the specification is checked at runtime against the implementation. Moreover, violations and/or validations of specifications can trigger user-defined code at any points in the program, in particular recovery code, outputting or sending messages, or raising exceptions. The MOP paradigm does not promote or enforce any specific formalism to specify requirements: it allows the users to plug-in their favorite or domain-specific specification formalisms via logic plug-in modules. There are two major technical challenges that MOP supporting tools unavoidably face: monitor synthesis and monitor integration. The former is heavily dependent on the specification formalism and comes as part of the corresponding logic plug-in, while the latter is uniform for all specification formalisms and depends only on the target programming language. An experimental prototype tool, called Java-MOP, is also discussed, which currently supports most but not all of the desired MOP features. MOP aims at reducing the gap between formal specification and implementation, by integrating the two and allowing them together to form a system

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

Enhancing the Compilation of Synchronous Dataflow Programs with a Combined Numerical-Boolean Abstraction

RR version = http://hal.inria.fr/hal-00780521/enInternational audienceIn this paper, we propose an enhancement of the compilation of synchronous programs with a combined numerical-Boolean abstraction. While our approach applies to synchronous dataflow languages in general, here, we consider the SIGNAL language for illustration. In the new abstraction, every signal in a program is associated with a pair of the form ( clock, value ), where clock is a Boolean function and value is a Boolean or numeric function. Given the performance level reached by recent progress in Satisfiability Modulo Theory (SMT), we use an SMT solver to reason on this abstraction. Through sample examples, we show how our solution is used to determine absence of reaction captured by empty clocks; mutual exclusion captured by two or more clocks whose associated signals never occur at the same time; or hierarchical control of component activations via clock inclusion. We also show that the analysis improves the quality of the code generated automatically by a compiler, e.g., a code with smaller footprint, or a code executed more efficiently thanks to optimizations enabled by the new abstraction. The implementation of the whole approach includes a translator of synchronous programs towards the standard input format of SMT solvers, and an ad hoc SMT solver that integrates advanced functionalities to cope with the issues of interest in this wor

Synthesizing Functional Reactive Programs

Functional Reactive Programming (FRP) is a paradigm that has simplified the construction of reactive programs. There are many libraries that implement incarnations of FRP, using abstractions such as Applicative, Monads, and Arrows. However, finding a good control flow, that correctly manages state and switches behaviors at the right times, still poses a major challenge to developers. An attractive alternative is specifying the behavior instead of programming it, as made possible by the recently developed logic: Temporal Stream Logic (TSL). However, it has not been explored so far how Control Flow Models (CFMs), as synthesized from TSL specifications, can be turned into executable code that is compatible with libraries building on FRP. We bridge this gap, by showing that CFMs are indeed a suitable formalism to be turned into Applicative, Monadic, and Arrowized FRP. We demonstrate the effectiveness of our translations on a real-world kitchen timer application, which we translate to a desktop application using the Arrowized FRP library Yampa, a web application using the Monadic threepenny-gui library, and to hardware using the Applicative hardware description language ClaSH.Comment: arXiv admin note: text overlap with arXiv:1712.0024

Special section on advances in reachability analysis and decision procedures: contributions to abstraction-based system verification

Reachability analysis asks whether a system can evolve from legitimate initial states to unsafe states. It is thus a fundamental tool in the validation of computational systems - be they software, hardware, or a combination thereof. We recall a standard approach for reachability analysis, which captures the system in a transition system, forms another transition system as an over-approximation, and performs an incremental fixed-point computation on that over-approximation to determine whether unsafe states can be reached. We show this method to be sound for proving the absence of errors, and discuss its limitations for proving the presence of errors, as well as some means of addressing this limitation. We then sketch how program annotations for data integrity constraints and interface specifications - as in Bertrand Meyers paradigm of Design by Contract - can facilitate the validation of modular programs, e.g., by obtaining more precise verification conditions for software verification supported by automated theorem proving. Then we recap how the decision problem of satisfiability for formulae of logics with theories - e.g., bit-vector arithmetic - can be used to construct an over-approximating transition system for a program. Programs with data types comprised of bit-vectors of finite width require bespoke decision procedures for satisfiability. Finite-width data types challenge the reduction of that decision problem to one that off-the-shelf tools can solve effectively, e.g., SAT solvers for propositional logic. In that context, we recall the Tseitin encoding which converts formulae from that logic into conjunctive normal form - the standard format for most SAT solvers - with only linear blow-up in the size of the formula, but linear increase in the number of variables. Finally, we discuss the contributions that the three papers in this special section make in the areas that we sketched above. © Springer-Verlag 2009