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Examples of naturalLess()

edu.cmu.sphinx.fst.semiring.Semiring.naturalLess()
NATURAL ORDER By definition: a <= b iff a + b = a The natural order is a negative partial order iff the semiring is idempotent. It is trivially monotonic for plus. It is left (resp. right) monotonic for times iff the semiring is left (resp. right) distributive. It is a total order iff the semiring has the path property. See Mohri, "Semiring Framework and Algorithms for Shortest-Distance Problems", Journal of Automata, Languages and Combinatorics 7(3):321-350, 2002. We define the strict version of this order below.

Examples of edu.cmu.sphinx.fst.semiring.Semiring.naturalLess()

                        float d2 = d[o2.getLeft().getId()];


                        float a1 = semiring.times(next, d2);
                        float a2 = semiring.times(previous, d1);


                        if (semiring.naturalLess(a1, a2))
                            return 1;


                        if (a1 == a2)
                            return 0;

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