Formal Methods of Software Design, Eric Hehner, segment 19 page 1 out of 3 [1] In this lecture I continue with the formal treatment of features that are common to many programming languages. And the first one this lecture is the result expression. It’s a way of using ifs and loops and all the state […]
CS124 Lecture 6 Spring 2011 Disjoint set (Union-Find) For Kruskal’s algorithm for the minimum spanning tree problem, we found that we needed a data structure for maintaining a collection of disjoint sets. That is, we need a data structure that can handle the following operations: • MAKESET(x) – create a new set containing the single
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Formal Methods of Software Design, Eric Hehner, segment 29 page 1 out of 4 [1] We have done a lot of programming and proving without concurrency. In this lecture, I want to show you how concurrency can be introduced automatically. We can write our programs as usual, and let the compiler transform them for concurrent
Formal Methods of Software Design, Eric Hehner, segment 15 page 1 out of 3 [talking head] So far, we have a very small set of programming notations. We have ok, for doing nothing. We have assignment, for changing the value of a variable. We have if-then- else-fi, for making a choice. And we have dependent
CS124 Lecture 4 Spring 2011 Breadth-First Search A searching technique with different properties than DFS is Breadth-First Search (BFS). While DFS used an implicit stack, BFS uses an explicit queue structure in determining the order in which vertices are searched. Also, generally one does not restart BFS, because BFS only makes sense in the context
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CS124 Lecture 5 Spring 2011 Minimum Spanning Trees A tree is an undirected graph which is connected and acyclic. It is easy to show that if graph G(V,E) that satisfies any two of the following properties also satisfies the third, and is therefore a tree: • G(V,E) is connected • G(V,E) is acyclic • |E|=|V|−1
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CS 124 Course Notes 1 Spring 2011 An algorithm is a recipe or a well-defined procedure for performing a calculation, or in general, for transforming some input into a desired output. Perhaps the most familiar algorithms are those those for adding and multiplying integers. Here is a multiplication algorithm that is different from the standard
CS 124 Lecture 2 In order to discuss algorithms effectively, we need to start with a basic set of tools. Here, we explain these tools and provide a few examples. Rather than spend time honing our use of these tools, we will learn how to use them by applying them in our studies of actual
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Interaction shared variables can be read and written by any process (most interaction) difficult to implement difficult to reason about interactive variables can be read by any process, written by only one process (some interaction) easier to implement easier to reason about boundary variables can be read and written by only one process (least interaction)
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CS124 Lecture 3 Spring 2011 Graphs and modeling Formulating a simple, precise specification of a computational problem is often a prerequisite to writing a computer program for solving the problem. Many computational problems are best stated in terms of graphs. A directed graph G(V,E) consists of a finite set of vertices V and a set
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