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504
Korat: Automated testing based on Java predicates
 IN PROC. INTERNATIONAL SYMPOSIUM ON SOFTWARE TESTING AND ANALYSIS (ISSTA
, 2002
"... This paper presents Korat, a novel framework for automated testing of Java programs. Given a formal specification for a method, Korat uses the method precondition to automatically generate all nonisomorphic test cases bounded by a given size. Korat then executes the method on each of these test case ..."
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Cited by 278 (51 self)
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This paper presents Korat, a novel framework for automated testing of Java programs. Given a formal specification for a method, Korat uses the method precondition to automatically generate all nonisomorphic test cases bounded by a given size. Korat then executes the method on each of these test cases, and uses the method postcondition as a test oracle to check the correctness of each output. To generate test cases for a method, Korat constructs a Java predicate (i.e., a method that returns a boolean) from the method’s precondition. The heart of Korat is a technique for automatic test case generation: given a predicate and a bound on the size of its inputs, Korat generates all nonisomorphic inputs for which the predicate returns true. Korat exhaustively explores the input space of the predicate but does so efficiently by monitoring the predicate’s executions and pruning large portions of the search space. This paper illustrates the use of Korat for testing several data structures, including some from the Java Collections Framework. The experimental results show that it is feasible to generate test cases from Java predicates, even when the search space for inputs is very large. This paper also compares Korat with a testing framework based on declarative specifications. Contrary to our initial expectation, the experiments show that Korat generates test cases much faster than the declarative framework.
GFUN: A Maple Package for the Manipulation of Generating and Holonomic Functions in One Variable
, 1992
"... We describe the gfun package which contains functions for manipulating sequences, linear recurrences or di erential equations and generating functions of various types. This document isintended both as an elementary introduction to the subject and as a reference manual for the package. ..."
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Cited by 142 (18 self)
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We describe the gfun package which contains functions for manipulating sequences, linear recurrences or di erential equations and generating functions of various types. This document isintended both as an elementary introduction to the subject and as a reference manual for the package.
Generating Trees and the Catalan and Schröder Numbers
 DEPARTMENT OF MATHEMATICS, STOCKHOLMS UNIVERSITET, S106 91
, 1995
"... A permutation 2 Sn avoids the subpattern iff has no subsequence having all the same pairwise comparisons as , and we write 2 Sn ( ). We present a new bijective proof of the wellknown result that jS n (123)j = jS n (132)j = c n , the nth Catalan number. A generalization to forbidden pattern ..."
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Cited by 103 (3 self)
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A permutation 2 Sn avoids the subpattern iff has no subsequence having all the same pairwise comparisons as , and we write 2 Sn ( ). We present a new bijective proof of the wellknown result that jS n (123)j = jS n (132)j = c n , the nth Catalan number. A generalization to forbidden patterns of length 4 gives an asymptotic formula for the vexillary permutations. We settle a conjecture of Shapiro and Getu that jS n (3142; 2413)j = s n\Gamma1 , the Schröder number, and characterize the dequesortable permutations of Knuth, also counted by s n\Gamma1 .
Generalized pattern avoidance
 European J. Combin
"... Abstract. Recently, Babson and Steingrímsson have introduced generalised permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We will consider pattern avoidance for such patterns, and give a complete solution for the number of pe ..."
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Cited by 74 (5 self)
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Abstract. Recently, Babson and Steingrímsson have introduced generalised permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We will consider pattern avoidance for such patterns, and give a complete solution for the number of permutations avoiding any single pattern of length three with exactly one adjacent pair of letters. For eight of these twelve patterns the answer is given by the Bell numbers. For the remaining four the answer is given by the Catalan numbers. We also give some results for the number of permutations avoiding two different patterns. These results relate the permutations in question to Motzkin paths, involutions and nonoverlapping partitions. Furthermore, we define a new class of set partitions, called monotone partitions, and show that these partitions are in onetoone correspondence with nonoverlapping partitions. 1.
Generating Functions for Generating Trees
 PROCEEDINGS OF 11TH FORMAL POWER SERIES AND ALGEBRAIC COMBINATORICS
, 1999
"... Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the object. Generating trees lead to a fast computation of enumerati ..."
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Cited by 68 (18 self)
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Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the object. Generating trees lead to a fast computation of enumeration sequences (sometimes, to explicit formulae as well) and provide efficient random generation algorithms. We investigate the links between the structural properties of the rewriting rules defining such trees and the rationality, algebraicity, or transcendence of the corresponding generating function.
Special Values of Multiple Polylogarithms
 Sém. Bourbaki, 53 e année, 2000–2001, n ◦ 885, Mars 2001; Astéisque 282 (2002
"... Abstract. Historically, the polylogarithm has attracted specialists and nonspecialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and highenergy physics. More recen ..."
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Cited by 59 (18 self)
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Abstract. Historically, the polylogarithm has attracted specialists and nonspecialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and highenergy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove several previously conjectured evaluations, including an intriguing conjecture of Don Zagier. 1.
Basic Analytic Combinatorics of Directed Lattice Paths
 Theoretical Computer Science
, 2001
"... This paper develops a unified enumerative and asymptotic theory of directed 2dimensional lattice paths in halfplanes and quarterplanes. The lattice paths are speci ed by a finite set of rules that are both time and space homogeneous, and have a privileged direction of increase. (They are then ess ..."
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Cited by 59 (11 self)
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This paper develops a unified enumerative and asymptotic theory of directed 2dimensional lattice paths in halfplanes and quarterplanes. The lattice paths are speci ed by a finite set of rules that are both time and space homogeneous, and have a privileged direction of increase. (They are then essentially 1dimensional objects.) The theory relies on a specific "kernel method" that provides an important decomposition of the algebraic generating functions involved, as well as on a generic study of singularities of an associated algebraic curve. Consequences are precise computable estimates for the number of lattice paths of a given length under various constraints (bridges, excursions, meanders) as well as a characterization of the limit laws associated to several basic parameters of paths.
classes of tautological sheaves on Hilbert schemes of points on surfaces
 Invent. Math
, 1999
"... We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on a smooth surface within the framework of Nakajima’s oscillator algebra. This leads to an identification of the cohomology ring of Hilb n (A 2) with a ring o ..."
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Cited by 49 (1 self)
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We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on a smooth surface within the framework of Nakajima’s oscillator algebra. This leads to an identification of the cohomology ring of Hilb n (A 2) with a ring of explicitly given differential operators on a Fock space. We end with the computation of the top Segre classes of tautological bundles associated to line bundles on Hilb n up to n = 7, extending computations of Severi, LeBarz, Tikhomirov and Troshina and give a conjecture for the generating series.