42,183 research outputs found
Program transformations using temporal logic side conditions
This paper describes an approach to program optimisation based on transformations, where temporal logic is used to specify side conditions, and strategies are created which expand the repertoire of transformations and provide a suitable level of abstraction. We demonstrate the power of this approach by developing a set of optimisations using our transformation language and showing how the transformations can be converted into a form which makes it easier to apply them, while maintaining trust in the resulting optimising steps. The approach is illustrated through a transformational case study where we apply several optimisations to a small program
Partial Quantifier Elimination By Certificate Clauses
We study partial quantifier elimination (PQE) for propositional CNF formulas.
In contrast to full quantifier elimination, in PQE, one can limit the set of
clauses taken out of the scope of quantifiers to a small subset of target
clauses. The appeal of PQE is twofold. First, PQE can be dramatically simpler
than full quantifier elimination. Second, it provides a language for performing
incremental computations. Many verification problems (e.g. equivalence checking
and model checking) are inherently incremental and so can be solved in terms of
PQE. Our approach is based on deriving clauses depending only on unquantified
variables that make the target clauses . Proving redundancy
of a target clause is done by construction of a ``certificate'' clause implying
the former. We describe a PQE algorithm called that employs
the approach above. We apply to generating properties of a
design implementation that are not implied by specification. The existence of
an property means that this implementation is buggy. Our
experiments with HWMCC-13 benchmarks suggest that can be used
for generating properties of real-life designs
Partial Quantifier Elimination
We consider the problem of Partial Quantifier Elimination (PQE). Given
formula exists(X)[F(X,Y) & G(X,Y)], where F, G are in conjunctive normal form,
the PQE problem is to find a formula F*(Y) such that F* & exists(X)[G] is
logically equivalent to exists(X)[F & G]. We solve the PQE problem by
generating and adding to F clauses over the free variables that make the
clauses of F with quantified variables redundant. The traditional Quantifier
Elimination problem (QE) is a special case of PQE where G is empty so all
clauses of the input formula with quantified variables need to be made
redundant. The importance of PQE is twofold. First, many problems are more
naturally formulated in terms of PQE rather than QE. Second, in many cases PQE
can be solved more efficiently than QE. We describe a PQE algorithm based on
the machinery of dependency sequents and give experimental results showing the
promise of PQE
The integration of systems of linear PDEs using conservation laws of syzygies
A new integration technique is presented for systems of linear partial
differential equations (PDEs) for which syzygies can be formulated that obey
conservation laws. These syzygies come for free as a by-product of the
differential Groebner Basis computation. Compared with the more obvious way of
integrating a single equation and substituting the result in other equations
the new technique integrates more than one equation at once and therefore
introduces temporarily fewer new functions of integration that in addition
depend on fewer variables. Especially for high order PDE systems in many
variables the conventional integration technique may lead to an explosion of
the number of functions of integration which is avoided with the new method. A
further benefit is that redundant free functions in the solution are either
prevented or that their number is at least reduced.Comment: 26 page
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