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text/bg-mwp.tex

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@@ -72,7 +72,7 @@ \subsubsection{Tracking Value Growth With Coefficients}
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If a command \pr|C|\symbo{p2} computes a function growing exponentially, the statement \(\prm{C} : M\) will be false for all matrices \(M\)\symbo{matrix}.
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The flow calculus\index{mwp-calculus} result is sound but incomplete.
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If a derivable\index{derivability} program terminates\index{termination},
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the soundness theorem~\cite[p. 11]{jones2009} guarantees that the variable value growth is polynomially bounded.
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the soundness theorem~\cite[p. 12]{jones2009} guarantees that the variable value growth is polynomially bounded.
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\begin{theorem}[{Soundness of mwp-calculus}]
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\label{mwp-soundness}\index{soundness of mwp-calculus}

text/ch-aims.tex

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@@ -237,7 +237,7 @@ \subsection{Dissertation Goals}\label{subsec:specific-aims}
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\ndx{expressiveness}. A common strategy is to show that the newly presented
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system gives a guarantee for some subset of programs that were not expressible
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previously.\footnote{The strategy is used \eg in~\cite[p.16--17]{hainry2023},
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~\cite[p. 17]{jones2009}, and~\cite[p. 147]{feree2018}.} However, this strategy
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~\cite[p. 18]{jones2009}, and~\cite[p. 147]{feree2018}.} However, this strategy
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is limited in quantifying practical usefulness of the ICC systems. Particularly,
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it does not account for the \enquote{methodological cost} at which the
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improvement is achieved. Applications would provide complementary insight and

text/ch-discussion.tex

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@@ -377,7 +377,7 @@ \subsection{Questions About the Flow Calculus}
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\begin{itemize}
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\item \emph{Have the developments changed the complexity of the derivability
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problem?}\footnote{The problem is \ccx{np}-complete by~\cite[p.
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37]{jones2009}).}
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40]{jones2009}).}
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The manuscripts in \autoref{sec:fscd},~\autoref{sec:atva},
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and~\autoref{sec:postcond} alter the inference procedure, therefore the
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answer is not obvious.

text/pubs-pc.tex

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@@ -325,7 +325,7 @@ \subsubsection{Conceptual primer of the flow calculus}
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\emph{\ndx{mwp-bound}} to every variable of a derivable program. An
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\ndx{mwp-bound} is an expression, in terms of the inputs, that characterizes the
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value growth of a single variable. If a derivable program terminates, the
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soundness theorem of the flow calculus~\cite[p. 11]{jones2009}\index{soundness
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soundness theorem of the flow calculus~\cite[p. 12]{jones2009}\index{soundness
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of mwp-calculus}\index{mwp-calculus} guarantees that the variable value growth
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is polynomially-bounded. The result is sound but not complete, \ie not all
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satisfactory programs can be captured, but on success we can prove the result
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derivable.\index{derivability} The rule E3 says \enquote{the vector of the left
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operand is multiplied by a polynomial coefficient.} The
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\(p\)\symbo{p}-coefficient tracks the fact that certain data flow patterns might
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not be polynomially bounded~\cite[p. 13]{jones2009}. Applying the rules to a
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not be polynomially bounded~\cite[p. 14]{jones2009}. Applying the rules to a
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vector propagates the effect to all variables that are transitively dependent on
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the left operand. Rule E4 is similar to E3, except the \(p\)\symbo{p}
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coefficient is applied to the right operand. Thus, three different derivation
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\noindent Variable query is safe for derivable programs\index{derivability},
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because all variables are guaranteed to have an \ndx{mwp-bound} by the soundness
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theorem of the flow calculus~\cite[p. 11]{jones2009}.\index{soundness of
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theorem of the flow calculus~\cite[p. 12]{jones2009}.\index{soundness of
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mwp-calculus} Additional caution is needed when a program is not derivable.
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\subsubsection{Variable mwp-bounds in presence of failure}

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