19 research outputs found

    Types of Depth and Formula Size

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    Counting and Gröbner Bases

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    We show how the complexity of counting relates to the well known phenomenon that computing Gröbner bases under a lexicographic order is generally harder than total degree orders. We give simple examples of polynomials for which it is very easy to compute their Gröbner basis using a total degree order but for which exponential time is required for a lexicographic order. It follows that conversion algorithms do not help in such cases

    Schenck, H.

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    Decision problems in group theory

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    At the 1976 Oxford Conference, Aanderaa introduced a new class of machines which he called F machines (later renamed as modular machines). Using these he gave two remarkably short and easy examples of finitely presented groups with unsolvable word problem. Both of these examples, together with an exposition of modula

    Decision Problems in Group Theory

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    EXPONENTIAL LENGTH OF CERTAIN SEQUENCES OF SUBSETS

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