New problems complete for nondeterministic log space

  title={New problems complete for nondeterministic log space},
  author={Neil D. Jones and Y. Edmund Lien and William T. Laaser},
  journal={Mathematical systems theory},
It is shown that a variety of problems have computational complexity equivalent to that of finding a path through a directed graph. These results, which parallel those of Karp at a lower complexity level, concern satisfiability of propositional formulas with two literals per clause, generation of elements by an associative binary operation, solution of linear equations with two variables per equation, equivalence of generalized sequential machines with final states, and deciding theLL(k) andLR… 
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This work raises the issue of limiting the number of final states in the automata intersection problem, and considers idempotent commutative automata and group automata with one, two, or three final states over a singleton or larger alphabet, elucidating the complexity of the intersection nonemptiness and related problems in each case.
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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
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Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
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