Abstract
Boolean satisfiability (k-SAT) is an NP-complete (k ≥ 3) problem that constitute one of the hardest classes of constraint satisfaction problems. In this work, we provide a proof of concept hardware based analog k-SAT solver, that is built using Magnetic Tunnel Junctions (MTJs). The inherent physics of MTJs, enhanced by device level modifications, is harnessed here to emulate the intricate dynamics of an analog satisfiability (SAT) solver. In the presence of thermal noise, the MTJ based system can successfully solve Boolean satisfiability problems. Most importantly, our results exhibit that, the proposed MTJ based hardware SAT solver is capable of finding a solution to a significant fraction (at least 85%) of hard 3-SAT problems, within a time that has a polynomial relationship with the number of variables(<50).
Highlights
Where xi∈{0, 1} is a variable and each clause is the disjunction (OR, ∪) of k (k = 3 in this case) such variables or their negation (xi)
This bounded system does not have polynomial time complexity, noise effects in the analog hardware can potentially reduce the long transient times[9] in the system, as we demonstrate in this work
We present a hardware platform built on nano-scale spintronic devices, which can successfully emulate the behaviour of the aforementioned SAT solver
Summary
Our numerical results demonstrate that, the MTJ based SAT solver exhibits a polynomial dependency, between the number of variables and the real time for convergence, even for SAT problems that are known to be hardest to solve (note that this is not a mathematical proof that shows a guaranteed polynomial time complexity). We conjecture that, this is due to the non-deterministic nature of our system caused by the random thermal noise, and due to the added complexities associated with MTJs
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