34 verified PDFs
The formulas link arithmetic on numbers to operations on types, with the num- ber 0 corresponding to the empty set (written ⊥ in Agda), 1 to a singleton set. ( ...
A data structure is linear if every item is related (or attached) to its previous and next item. Linear Data Items are arranged in a linear sequence. Linear ...
A recursive equation is a functional equation of some unknown function T : N → R+, where T(n) is given in terms of one or more T(ki), with ki < ...
Our example shows a verification condition formula generated when verifying an unbounded linked data structure. The formula belongs to our new decidable.
A sequence of instructions to the computer, written in a programming language, somewhat like English, but very much simpler - and very much stricter. This ...
Space complexity. 2. Time complexity. Analysis of space complexity of an algorithm or program is the amount of memory it needs to run to completion. Some of ...
Example 2.1. For example consider this simple block of code which sorts a pair of distinct values: \\ PRE: A is an array of two distinct ...
Expectation: If X is discrete. E[g(X)] = Xx g(x) Pr[X = x]. If X continuous then. E[g(X)] = Z. ∞. −∞g(x)p(x) dx = Z. ∞. −∞ g(x) dP(x). Variance, standard ...
Propositional Connectives and Quantifiers. Logical notation uses symbols of two kinds: propositional connectives, such as. ∧ (“and”), ∨ (“or”), ¬ (“not”),.
When we analyze an algorithm A for a specific problem, we want to char- acterize the running time of A as a function of its input (and later only of the input ...
We show how tree-like data structures (B-trees, AVL trees, binary trees, etc....) can be characterizod by functional equations in the context of the theory of ...
The finite element method generates systems of linear equations having tens of thousands of var~ables and one hundred or so non-zero coefficients per equation.
The study of data structures has long been considered the cornerstone and starting point for the systematic examination of computer science as a discipline.
Abstract: We introduce the notion of generic examples as a uniting principle for various phenomena in computer science such as initial structures in the ...
