Trees in informal methods
What’s a tree? First define a sequence or length n> 0 as a total map s: {1,.. n}→ X. Let Nil be the empty sequence. If s is a sequence of length n, and x is an element, then u
Linked lists
What’s a linked list? Let V be a set of values and A be a set of “addresses”. Say a map f is a “linked list element” compatible with values V and addresses A if and only if f(value)∈ V
informal methods applied to networks and timeouts
Distributed computation involves many interesting issues concerning shared data. Here I want to sketch out what networks look like using applied (informal) mathematics so we can look at some algorithms for consensus and data consistency. No formal methods or category
Sorting and groups
I can’t find much reference to this in the literature (see Maus for some hints and an interesting paper) , but surely people have looked at sorting as a problem in group theory? Given a sequence $latex s=[x_1\dots x_n] $
state equations in practice
When people think of mathematical models of state for programs and other computer systems, it’s natural and conventional to consider state as a map from symbolic names of state variable to values. This is an error for a number
State equations
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A mathematical basis for understanding software modularity
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Practical State Machines for Computer Software and Engineering
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more on missed wakeup
Here are some conventions [Update: typos fix, Friday] We are concerned with state machines and sequences of events. The prefixes of a sequence include the empty sequence “null” and the sequence itself. Relative state: If “w” is the sequence of