Safe Spacecraft Rendezvous and Proximity Operations via Reachability Analysis

The rapid expansion of the utilization of space by nations and industry has presented new challenges and opportunities to operate efficiently and responsibly. Reachability analysis is the process of computing the set of states that can be reached given all admissible controls and can be a valuable component in an autonomous mission planning system if conducted efficiently. In the current research, reachability analysis is used with several relative motion models to show that all ranges of orbits can be computed in milliseconds, and that it is a feasible approach for on-board autonomous mission planning. Reachability analysis is then combined with an Artificial Potential Function (APF) derived guidance control law to conduct safe spacecraft rendezvous between a deputy in a Natural Motion Circumnavigation (NMC) relative orbit around a chief while avoiding obstacles. While the APF employed in this research requires improvements for trajectory computation, this research demonstrates the feasibility of combining reachability analysis with an APF for safe, on-board, autonomous mission planning

Sketch-based Influence Maximization and Computation: Scaling up with Guarantees

Propagation of contagion through networks is a fundamental process. It is used to model the spread of information, influence, or a viral infection. Diffusion patterns can be specified by a probabilistic model, such as Independent Cascade (IC), or captured by a set of representative traces. Basic computational problems in the study of diffusion are influence queries (determining the potency of a specified seed set of nodes) and Influence Maximization (identifying the most influential seed set of a given size). Answering each influence query involves many edge traversals, and does not scale when there are many queries on very large graphs. The gold standard for Influence Maximization is the greedy algorithm, which iteratively adds to the seed set a node maximizing the marginal gain in influence. Greedy has a guaranteed approximation ratio of at least (1-1/e) and actually produces a sequence of nodes, with each prefix having approximation guarantee with respect to the same-size optimum. Since Greedy does not scale well beyond a few million edges, for larger inputs one must currently use either heuristics or alternative algorithms designed for a pre-specified small seed set size. We develop a novel sketch-based design for influence computation. Our greedy Sketch-based Influence Maximization (SKIM) algorithm scales to graphs with billions of edges, with one to two orders of magnitude speedup over the best greedy methods. It still has a guaranteed approximation ratio, and in practice its quality nearly matches that of exact greedy. We also present influence oracles, which use linear-time preprocessing to generate a small sketch for each node, allowing the influence of any seed set to be quickly answered from the sketches of its nodes.Comment: 10 pages, 5 figures. Appeared at the 23rd Conference on Information and Knowledge Management (CIKM 2014) in Shanghai, Chin

Formal verification of safety properties in timed circuits

The incorporation of timing makes circuit verification computationally expensive. This paper proposes a new approach for the verification of timed circuits. Rather than calculating the exact timed stare space, a conservative overestimation that fulfills the property under verification is derived. Timing analysis with absolute delays is efficiently performed at the level of event structures and transformed into a set of relative timing constraints. With this approach, conventional symbolic techniques for reachability analysis can be efficiently combined with timing analysis. Moreover the set of timing constraints used to prove the correctness of the circuit can also be reported for backannotation purposes. Some preliminary results obtained by a naive implementation of the approach show that systems with more than 10/sup 6/ untimed states can be verified.Peer ReviewedPostprint (published version

Safety Model Checking with Complementary Approximations

Formal verification techniques such as model checking, are becoming popular in hardware design. SAT-based model checking techniques such as IC3/PDR, have gained a significant success in hardware industry. In this paper, we present a new framework for SAT-based safety model checking, named Complementary Approximate Reachability (CAR). CAR is based on standard reachability analysis, but instead of maintaining a single sequence of reachable- state sets, CAR maintains two sequences of over- and under- approximate reachable-state sets, checking safety and unsafety at the same time. To construct the two sequences, CAR uses standard Boolean-reasoning algorithms, based on satisfiability solving, one to find a satisfying cube of a satisfiable Boolean formula, and one to provide a minimal unsatisfiable core of an unsatisfiable Boolean formula. We applied CAR to 548 hardware model-checking instances, and compared its performance with IC3/PDR. Our results show that CAR is able to solve 42 instances that cannot be solved by IC3/PDR. When evaluated against a portfolio that includes IC3/PDR and other approaches, CAR is able to solve 21 instances that the other approaches cannot solve. We conclude that CAR should be considered as a valuable member of any algorithmic portfolio for safety model checking

Combining Forward and Backward Abstract Interpretation of Horn Clauses

Alternation of forward and backward analyses is a standard technique in abstract interpretation of programs, which is in particular useful when we wish to prove unreachability of some undesired program states. The current state-of-the-art technique for combining forward (bottom-up, in logic programming terms) and backward (top-down) abstract interpretation of Horn clauses is query-answer transformation. It transforms a system of Horn clauses, such that standard forward analysis can propagate constraints both forward, and backward from a goal. Query-answer transformation is effective, but has issues that we wish to address. For that, we introduce a new backward collecting semantics, which is suitable for alternating forward and backward abstract interpretation of Horn clauses. We show how the alternation can be used to prove unreachability of the goal and how every subsequent run of an analysis yields a refined model of the system. Experimentally, we observe that combining forward and backward analyses is important for analysing systems that encode questions about reachability in C programs. In particular, the combination that follows our new semantics improves the precision of our own abstract interpreter, including when compared to a forward analysis of a query-answer-transformed system.Comment: Francesco Ranzato. 24th International Static Analysis Symposium (SAS), Aug 2017, New York City, United States. Springer, Static Analysi