• Corpus ID: 232134900

The Clifford algebra of $R^{n,n}$ and the Boolean Satisfiability Problem

@inproceedings{Budinich2021TheCA,
  title={The Clifford algebra of \$R^\{n,n\}\$ and the Boolean Satisfiability Problem},
  author={Marco Budinich},
  year={2021}
}
We formulate a Boolean algebra in the set of idempotents of Clifford algebra Cl(R) and within this frame we examine different formulations of the Boolean Satisfiability Problem in Clifford algebra. Exploiting the isomorphism between null subspaces of R associated to simple spinors and the orthogonal group O(n) we ultimately give a continuous formulation of the Boolean Satisfiability Problem within this group that opens unexplored perspectives. 
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References

SHOWING 1-10 OF 20 REFERENCES
The Boolean SATisfiability Problem and the orthogonal group $O(n)$
We explore the relations between the Boolean Satisfiability Problem with $n$ literals and the orthogonal group $O(n)$ and show that all solutions lie in the compact and disconnected real manifold of…
The Boolean SATisfiability Problem in Clifford algebra
Reductions in Computational Complexity Using Clifford Algebras
Abstract.A number of combinatorial problems are treated using properties of abelian null-square-generated and idempotent-generated subalgebras of Clifford algebras. For example, the problem of…
A New Set of Independent Postulates for the Algebra of Logic with Special Reference to Whitehead and Russell's Principia Mathematica
Three sets of independent postulates for the algebra of logic, or Boolean algebra, were published by the present writer in 1904. The first set, based on the treatment in Whitehead's Universal…
On spinors transformations
We begin showing that for even dimensional vector spaces V all automorphisms of their Clifford algebras are inner. So all orthogonal transformations of V are restrictions to V of inner automorphisms…
The complexity of theorem-proving procedures
  • S. Cook
  • Mathematics, Computer Science
    STOC
  • 1971
It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a…
On Simple Spinors, Null Vectors and the Orthogonal Group O(n)
We explore the three separate isomorphisms that link together simple spinors, null vectors and the orthogonal group O(n) and exploit them to look back at these arguments from a unified viewpoint.
Survey propagation: An algorithm for satisfiability
TLDR
A new type of message passing algorithm is introduced which allows to find efficiently a satisfying assignment of the variables in this difficult region of randomly generated formulas.
Fock space description of simple spinors
Cartan’s simple—often called pure—spinors corresponding to even‐dimensional complex vector spaces are defined in terms of the associated maximal totally null planes. Their geometrical properties are…
An improved exponential-time algorithm for k-SAT
TLDR
A simple new randomized algorithm, called ResolveSat, for finding satisfying assignments of Boolean formulas in conjunctive normal form, which is the fastest known probabilistic algorithm for k-CNF satisfiability and proves a lower bound on the number of codewords of a code defined by a <i>k</i>-C NF.
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