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
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Process algebra is based on a misunderstanding of automata theory
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 over the alphabet.“ That’s not at
Practical State Machines for Computer Software and Engineering
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Theories of abstract automata – Arbib
We have said that automata theory deals with the realization of partial functions F: X* —» Y* by some finitely specifiable substrate. Before we specify in more detail the forms (of which the Turing machine is one) of substrate which
Algebra for computer science and function nesting
The fundamental mathematical basis of computer science is that code and data are the same things. A sequence of bits can represent real numbers, integers, vectors, groups, matrices, video , audio, or programs, algorithms or even proofs. When we try
Primitive recursion over words
From: @book{Peter:1982:RFC:539249, author = {Peter, Roezsa}, title = {Recursive Functions in Computer Theory}, year = {1982}, isbn = {0470271957}, publisher = {Halsted Press}, address = {New York, NY, USA}, }
Pointers draft
Despite pedants, pointers are useful and interesting and if you don’t understand them, you don’t really get what’s going on in a computer. Think of memory as a function $latex M: N\to N$ where $latex N$ is the set of
Fischer Lynch Patterson and timeouts
There is a widely cited (over 1400 cites in CiteseerX ) result called the Fischer-Lynch-Patterson theorem about consensus – a key issue in distributed databases or any system where data is either distributed or replicated or both. In this paper, we
A hard theorem becomes easy over time.
The basic result of the incompleteness proofs is pretty simple. The proofs are complicated because the idea was literally unthinkable until programming was invented. The heroic efforts of Gödel, Skolem, Post, and Church to create a mathematics in which doing mathematics