36,340 research outputs found
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
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