Generalization ALgorithms and Applications [GALA]

@techreport{RISC5918,
author = {David M. Cerna and Temur Kutsia},
title = {{Higher-Order Pattern Generalization Modulo Equational Theories with a unit element}},
language = {english},
abstract = {We consider anti-unification for simply typed lambda terms in theories defined by associativity,commutativity, identity (unit element) axioms and their combinations, and develop a sound andcomplete algorithm which takes two lambda terms and computes their equational generalizations inthe form of higher-order patterns. The problem is finitary: the minimal complete set of suchgeneralizations contains finitely many elements. We define the notion of optimal solution andinvestigate special fragments of the problem for which the optimal solution can be computed in linearor polynomial time.},
year = {2019},
length = {25},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

@techreport{RISC5939,
author = {Temur Kutsia and Cleo Pau},
title = {{Computing All Maximal Clique Partitions in a Graph}},
language = {english},
number = {19-04},
year = {2019},
length = {9},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

@techreport{RISC5950,
author = {Temur Kutsia and Cleo Pau},
title = {{Solving Proximity Constraints}},
language = {english},
number = {19-06},
year = {2019},
length = {21},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

@techreport{RISC5953,
author = {Temur Kutsia and Cleo Pau},
title = {{Matching and Generalization Modulo Proximity and Tolerance}},
language = {english},
number = {19-07},
year = {2019},
length = {5},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

@techreport{RISC5549,
author = {Alexander Baumgartner and Temur Kutsia and Jordi Levy and Mateu Villaret},
title = {{Term-Graph Anti-Unification}},
language = {english},
number = {18-02},
year = {2018},
length = {19},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

@techreport{RISC5982,
author = {David M. Cerna},
title = {{A General Recursive Construction for Schematic Resolution Derivations}},
language = {english},
abstract = {Proof schemata provide an alternative formalism for handling inductive argumentation, while non-trivially extending {\em Herbrand's theorem} to a fragment of arithmetic and thus allowing the construction of {\em Herbrand sequents} and {\em expansion trees}. Existing proof analysis methods for proof schemata extract an unsatisfiable characteristic formula representing the cut structure of the proof and from its refutation construct a Herbrand sequent. Unfortunately, constructing the refutation is a task which is highly non-trivial. An automated method for constructing such refutations exists, but it only works for a very weak fragment of arithmetic and is hard to use interactively. More expressive yet interactive methods for the formalization of recursive resolution refutation are complex, hard to work with, and still limited to an undesirably weak class of recursion. In this work we note a particular problem with previous methods, namely they mix the recursive structure with the calculus of refutation. Also we present a modular recursive structure independent of the resolution formalism and proof construction. We illustrate the expressive power of the so called {\em finite saturated tree} formalism by formalizing the Non-injectivity Assertion's schematic refutation (a variant of the infinitary Pigeonhole principle). None of the previously developed formalism are able to formalize this refutation.},
year = {2018},
length = {42},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}