A flow calculus of mwp-bounds for complexity analysis

We present a method for certifying that the values computed by an imperative program will be bounded by polynomials in the program's inputs. To this end, we introduce <i>mwp</i>-matrices and define a semantic relation ⊧ C : <i>M</i>, where C is a program and <i>M</i> is an <i>mwp</i>-matrix. It follows straightforwardly from our definitions that there exists <i>M</i> such that ⊧ C : <i>M</i> holds iff every value computed by C is bounded by a polynomial in the inputs. Furthermore, we provide a syntactical proof calculus and define the relation ⊢ C : <i>M</i> to hold iff there exists a derivation in the calculus where C : <i>M</i> is the bottom line. We prove that ⊢ C : <i>M</i> implies ⊧ C : <i>M</i>. By means of exhaustive proof search, an algorithm can decide if there exists <i>M</i> such that the relation ⊢ C : <i>M</i> holds, and thus, our results yield a computational method.

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