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] $
Basic math for basic algorithms
It’s odd that all the descriptions of basic programming operations, such as sorting, rely on pseudo code or complex formal logic. All we are doing is modifying finite sequences so it seems like we should be able to use ordinary
circularity problems in distributed consensus
Distributed consensus involves organizing a collection of independent agents – processes or network sites – to agree on some value or sequence of values. Many distributed consensus methods depend on a leader-follower scheme in which the leader is an agent
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
Download paper. Unable to display
Operations and maps on finite sequences
A lot of what I’m trying to do with mathematical models of computer systems involves operations on finite sequences. Define a “finite sequence of length n>0” to be any total map f: {1 … n} → X for some set X.
A mathematical basis for understanding software modularity
Download.
Process algebra is based on a misunderstanding of automata theory
See the current pdf in Arxiv Robin Milner’s book Communication and Concurrency involves a take on state machines that is fundamentally incorrect. “Now in standard automata theory, an automaton is interpreted as a language i.e. as a set of strings