Transfer Function Synthesis without Quantifier Elimination

Traditionally, transfer functions have been designed manually for each operation in a program, instruction by instruction. In such a setting, a transfer function describes the semantics of a single instruction, detailing how a given abstract input state is mapped to an abstract output state. The net effect of a sequence of instructions, a basic block, can then be calculated by composing the transfer functions of the constituent instructions. However, precision can be improved by applying a single transfer function that captures the semantics of the block as a whole. Since blocks are program-dependent, this approach necessitates automation. There has thus been growing interest in computing transfer functions automatically, most notably using techniques based on quantifier elimination. Although conceptually elegant, quantifier elimination inevitably induces a computational bottleneck, which limits the applicability of these methods to small blocks. This paper contributes a method for calculating transfer functions that finesses quantifier elimination altogether, and can thus be seen as a response to this problem. The practicality of the method is demonstrated by generating transfer functions for input and output states that are described by linear template constraints, which include intervals and octagons.Comment: 37 pages, extended version of ESOP 2011 pape

A Backward-traversal-based Approach for Symbolic Model Checking of Uniform Strategies for Constrained Reachability

Since the introduction of Alternating-time Temporal Logic (ATL), many logics have been proposed to reason about different strategic capabilities of the agents of a system. In particular, some logics have been designed to reason about the uniform memoryless strategies of such agents. These strategies are the ones the agents can effectively play by only looking at what they observe from the current state. ATL_ir can be seen as the core logic to reason about such uniform strategies. Nevertheless, its model-checking problem is difficult (it requires a polynomial number of calls to an NP oracle), and practical algorithms to solve it appeared only recently. This paper proposes a technique for model checking uniform memoryless strategies. Existing techniques build the strategies from the states of interest, such as the initial states, through a forward traversal of the system. On the other hand, the proposed approach builds the winning strategies from the target states through a backward traversal, making sure that only uniform strategies are explored. Nevertheless, building the strategies from the ground up limits its applicability to constrained reachability objectives only. This paper describes the approach in details and compares it experimentally with existing approaches implemented into a BDD-based framework. These experiments show that the technique is competitive on the cases it can handle.Comment: In Proceedings GandALF 2017, arXiv:1709.0176

Methods to Model-Check Parallel Systems Software

We report on an effort to develop methodologies for formal verification of parts of the Multi-Purpose Daemon (MPD) parallel process management system. MPD is a distributed collection of communicating processes. While the individual components of the collection execute simple algorithms, their interaction leads to unexpected errors that are difficult to uncover by conventional means. Two verification approaches are discussed here: the standard model checking approach using the software model checker SPIN and the nonstandard use of a general-purpose first-order resolution-style theorem prover OTTER to conduct the traditional state space exploration. We compare modeling methodology and analyze performance and scalability of the two methods with respect to verification of MPD.Comment: 12 pages, 3 figures, 1 tabl