3,711 research outputs found
A Framework for the Flexible Integration of a Class of Decision Procedures into Theorem Provers
The role of decision procedures is often essential in theorem proving. Decision procedures can reduce the search space of heuristic components of a prover and increase its abilities. However, in some applications only a small number of conjectures fall within the scope of the available decision procedures. Some of these conjectures could in an informal sense fall ‘just outside’ that scope. In these situations a problem arises because lemmas have to be invoked or the decision procedure has to communicate with the heuristic component of a theorem prover. This problem is also related to the general problem of how to exibly integrate decision procedures into heuristic theorem provers. In this paper we address such problems and describe a framework for the exible integration of decision procedures into other proof methods. The proposed framework can be used in different theorem provers, for different theories and for different decision procedures. New decision procedures can be simply ‘plugged-in’ to the system. As an illustration, we describe an instantiation of this framework within the Clam proof-planning system, to which it is well suited. We report on some results using this implementation
Transfer Function Synthesis without Quantifier Elimination
Traditionally, transfer functions have been designed manually for each
operation in a program, instruction by instruction. In such a setting, a
transfer function describes the semantics of a single instruction, detailing
how a given abstract input state is mapped to an abstract output state. The net
effect of a sequence of instructions, a basic block, can then be calculated by
composing the transfer functions of the constituent instructions. However,
precision can be improved by applying a single transfer function that captures
the semantics of the block as a whole. Since blocks are program-dependent, this
approach necessitates automation. There has thus been growing interest in
computing transfer functions automatically, most notably using techniques based
on quantifier elimination. Although conceptually elegant, quantifier
elimination inevitably induces a computational bottleneck, which limits the
applicability of these methods to small blocks. This paper contributes a method
for calculating transfer functions that finesses quantifier elimination
altogether, and can thus be seen as a response to this problem. The
practicality of the method is demonstrated by generating transfer functions for
input and output states that are described by linear template constraints,
which include intervals and octagons.Comment: 37 pages, extended version of ESOP 2011 pape
A Decidable Class of Nested Iterated Schemata (extended version)
Many problems can be specified by patterns of propositional formulae
depending on a parameter, e.g. the specification of a circuit usually depends
on the number of bits of its input. We define a logic whose formulae, called
"iterated schemata", allow to express such patterns. Schemata extend
propositional logic with indexed propositions, e.g. P_i, P_i+1, P_1, and with
generalized connectives, e.g. /\i=1..n or i=1..n (called "iterations") where n
is an (unbound) integer variable called a "parameter". The expressive power of
iterated schemata is strictly greater than propositional logic: it is even out
of the scope of first-order logic. We define a proof procedure, called DPLL*,
that can prove that a schema is satisfiable for at least one value of its
parameter, in the spirit of the DPLL procedure. However the converse problem,
i.e. proving that a schema is unsatisfiable for every value of the parameter,
is undecidable so DPLL* does not terminate in general. Still, we prove that it
terminates for schemata of a syntactic subclass called "regularly nested". This
is the first non trivial class for which DPLL* is proved to terminate.
Furthermore the class of regularly nested schemata is the first decidable class
to allow nesting of iterations, i.e. to allow schemata of the form /\i=1..n
(/\j=1..n ...).Comment: 43 pages, extended version of "A Decidable Class of Nested Iterated
Schemata", submitted to IJCAR 200
Métodos matemáticos e computacionais para modelagem e edição de deformações
Orientador: Jorge StolfiTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Nesta tese, descrevemos primeiramente o algoritmo ECLES (Editing by Constrained LEast Squares), um método geral para edição interativa de objetos definidos por parâmetros sujeitos a restrições lineares ou afins. Neste método, as restrições e as ações de edição do usuário são combinadas usando mÃnimos quadrados restritos, ao invés da abordagem mais comum de elementos finitos. Usamos aritmética exata para detectar e eliminar redundâncias no conjunto de restrições e evitar falhas devido a erros de arredondamento. O algoritmo ECLES tem diversas aplicações. Entre elas, podemos citar a edição de deformações spline com continuidade C¹. Nesta tese, descrevemos um método interativo de edição de deformações do plano, o algoritmo 2DSD (2D Spline Deformation). As deformações são definidas por splines de grau 5 sobre uma malha triangular arbitrária. Estas deformações são editadas alterando-se as posições dos pontos de controle da malha. O algoritmo ECLES é usado em cada ação de edição do usuário para detectar, de forma robusta e eficiente, o conjunto de restrições de continuidade C¹ que são relevantes, garantindo que não existam redundâncias. Em seguida, como os parâmetros são modificados pelo usuário, o ECLES é chamado para calcular as novas posições dos pontos de controle satisfazendo as restrições e as posições especificadas pelo usuário. A fim de validar nosso método 2DSD, ele foi utilizado como parte de um editor interativo para deformações do espaço 2.5D, o editor PrisMystic. Este editor foi utilizado, principalmente, para deformar modelos tridimensionais de organismos microscópicos não-rÃgidos de modo a coincidir com imagens reais de microscopia ótica. Também utilizamos o editor para editar modelos de terrenosAbstract: In this thesis, we present the ECLES algorithm (Editing by Constrained LEast Squares), a general method for interactive editing of objects that are defined by parameters subject to linear or affine constraints. In this method, the constraints and the user editing actions are combined using constrained least squares instead of the usual finite element approach. We use exact integer arithmetic in order to detect and eliminate redundancies in the set of constraints and to avoid failures due to rounding errors. The ECLES algorithm has various applications. Among them, we can cite the editing of C¹-continuous spline deformations. In this thesis, we describe an interactive editing method for deformations of the plane, the 2DSD algorithm (2D Spline Deformation). The deformations are defined by splines of degree 5 on an arbitrary triangular mesh. The deformations are edited by changing the positions of its control points. The ECLES algorithm is first used in each user editing action in order to detect, in a robust and efficient way, the set of relevant constraints of C¹ continuity, ensuring that there are no redundancies. Then, as the parameters are changed by the user, ECLES is called to compute the new positions of the control points satisfying the constraints and the positions specified by the user. To validate our 2DSD algorithm, we used it as part of an interactive editor for 2.5D space deformations, the PrisMystic editor. This editor has been used, mainly, to deform 3D models of non-rigid living microscopic organisms as seen in actual optical microscope images. We also used the editor to edit terrain modelsDoutoradoCiência da ComputaçãoDoutora em Ciência da Computação140780/2013-001-P-04554-2013CNPQCAPE
Hierarchic Superposition Revisited
Many applications of automated deduction require reasoning in first-order
logic modulo background theories, in particular some form of integer
arithmetic. A major unsolved research challenge is to design theorem provers
that are "reasonably complete" even in the presence of free function symbols
ranging into a background theory sort. The hierarchic superposition calculus of
Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we
demonstrate, not optimally. This paper aims to rectify the situation by
introducing a novel form of clause abstraction, a core component in the
hierarchic superposition calculus for transforming clauses into a form needed
for internal operation. We argue for the benefits of the resulting calculus and
provide two new completeness results: one for the fragment where all
background-sorted terms are ground and another one for a special case of linear
(integer or rational) arithmetic as a background theory
Hierarchic Superposition Revisited
Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory
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