Mohamad Noureddine

Mohamad Jaber, Mohamad Noureddine, Fadi A. Zaraket

Behavior-Interaction-Priority (BIP) is a layered embedded system design and verification framework that provides separation of functionality, synchronization, and priority concerns to simplify system design and to establish correctness by construction. The framework comes with a runtime engine and a suite of verification tools that uses D-Finder and NuSMV as model checkers. In this paper we provide a method and a supporting tool that takes a BIP system and a set of invariants and computes a reduced sequential circuit with a system-specific scheduler and with a designated output that is true when the invariants hold. Our method uses ABC, a sequential circuit synthesis and verification framework to (1) generate an efficient FPGA implementation of the system, and to (2) verify the system and debug it in case a counterexample was found. Moreover we generate a concurrent C implementation of the circuit that can be directly used as a simulator. We evaluated our method with two large systems and our results outperform those possible with existing techniques.

Fadi A. Zaraket, Mohamad Noureddine

Static verification techniques leverage Boolean formula satisfiability solvers such as SAT and SMT solvers that operate on conjunctive normal form and first order logic formulae, respectively, to validate programs. They force bounds on variable ranges and execution time and translate the program and its specifications into a Boolean formula. They are limited to programs of relatively low complexity for the following reasons. (1) A small increase in the bounds can cause a large increase in the size of the translated formula. (2) Boolean satisfiability solvers are restricted to using optimizations that apply at the level of the formula. Finally, (3) the Boolean formulae often need to be regenerated with higher bounds to ensure the correctness of the translation. We present a method that uses sequential circuits, Boolean formulae with memory elements and hierarchical structure, and sequential circuit synthesis and verification frameworks to validate programs. (1) Sequential circuits are much more succinct than Boolean formulae with no memory elements and preserve the high-level structure of the program. (2) Encoding the problem as a sequential circuit enables the use of a number of powerful automated analysis techniques that have no counterparts for other Boolean formulae. Our method takes an imperative program with a first order logic specification consisting of a precondition and a postcondition pair, and a bound on the program variable ranges, and produces a sequential circuit with a designated output that is true when the program violates the specification.

Paul C. Attie, Fadi A. Zaraket, Mohamad Noureddine et al.

We propose a method to write and check a specification including quantifiers using behaviors, i.e., input-output pairs. Our method requires the following input from the user: (1) answers to a finite number of queries, each of which presents some behavior to the user, who responds informing whether the behavior is "correct" or not; and (2) an "equivalence" theory (set of formulae), which represents the users opinion about which pairs of behaviors are equivalent with respect to the specification; and (3) a "vocabulary", i.e., a set of formulae which provide the basic building blocks for the specification to be written. Alternatively, the user can specify a type theory and a simple relational grammar, and our method can generate the vocabulary and equivalence theories. Our method automatically generates behaviors using a satisfiability modulo theory solver. Since writing a specification consists of formalizing ideas that are initially informal, there must, by definition, be at least one "initial" step where an informal notion is formalized by the user in an ad hoc manner. This step is the provision of the equivalence theory and vocabulary; we call it the primitive formalization step. We contend that it is considerably easier to write an equivalence theory and vocabulary than to write a full-blown formal specification from scratch, and we provide experimental evidence for this claim. We also show how vocabularies can be constructed hierarchically, with a specification at one level providing vocabulary material for the next level.