Probabilistic Model Counting with Short XORs

The idea of counting the number of satisfying truth assignments (models) of a formula by adding random parity constraints can be traced back to the seminal work of Valiant and Vazirani, showing that NP is as easy as detecting unique solutions. While theoretically sound, the random parity constraints in that construction have the following drawback: each constraint, on average, involves half of all variables. As a result, the branching factor associated with searching for models that also satisfy the parity constraints quickly gets out of hand. In this work we prove that one can work with much shorter parity constraints and still get rigorous mathematical guarantees, especially when the number of models is large so that many constraints need to be added. Our work is based on the realization that the essential feature for random systems of parity constraints to be useful in probabilistic model counting is that the geometry of their set of solutions resembles an error-correcting code.Comment: To appear in SAT 1

Mastermind is NP-Complete

In this paper we show that the Mastermind Satisfiability Problem (MSP) is NP-complete. The Mastermind is a popular game which can be turned into a logical puzzle called Mastermind Satisfiability Problem in a similar spirit to the Minesweeper puzzle. By proving that MSP is NP-complete, we reveal its intrinsic computational property that makes it challenging and interesting. This serves as an addition to our knowledge about a host of other puzzles, such as Minesweeper, Mah-Jongg, and the 15-puzzle

Security of GPS/INS based On-road Location Tracking Systems

Location information is critical to a wide-variety of navigation and tracking applications. Today, GPS is the de-facto outdoor localization system but has been shown to be vulnerable to signal spoofing attacks. Inertial Navigation Systems (INS) are emerging as a popular complementary system, especially in road transportation systems as they enable improved navigation and tracking as well as offer resilience to wireless signals spoofing, and jamming attacks. In this paper, we evaluate the security guarantees of INS-aided GPS tracking and navigation for road transportation systems. We consider an adversary required to travel from a source location to a destination, and monitored by a INS-aided GPS system. The goal of the adversary is to travel to alternate locations without being detected. We developed and evaluated algorithms that achieve such goal, providing the adversary significant latitude. Our algorithms build a graph model for a given road network and enable us to derive potential destinations an attacker can reach without raising alarms even with the INS-aided GPS tracking and navigation system. The algorithms render the gyroscope and accelerometer sensors useless as they generate road trajectories indistinguishable from plausible paths (both in terms of turn angles and roads curvature). We also designed, built, and demonstrated that the magnetometer can be actively spoofed using a combination of carefully controlled coils. We implemented and evaluated the impact of the attack using both real-world and simulated driving traces in more than 10 cities located around the world. Our evaluations show that it is possible for an attacker to reach destinations that are as far as 30 km away from the true destination without being detected. We also show that it is possible for the adversary to reach almost 60-80% of possible points within the target region in some cities

Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

An optical solution for the set splitting problem

We describe here an optical device, based on time-delays, for solving the set splitting problem which is well-known NP-complete problem. The device has a graph-like structure and the light is traversing it from a start node to a destination node. All possible (potential) paths in the graph are generated and at the destination we will check which one satisfies completely the problem's constrains.Comment: 10 pages, 2 figure