Sequence-Based Specification (SBS)

If you have been given access to work on the advanced SBS work, click here...

Axioms

Lets develop an axiomatic formulation for sequence enumeration and abstraction. There are several goals for this work.

  • Unify sequence enumeration and sequence abstraction. Read more...
  • Develop the mathematics for composition of enumerations. Read more...
  • If possible, identify a classification system for abstractions based on formal properties. Read more...
  • Correctly incorporate advanced refinement techniques such as interrupts. Read more...

This should lead to cleaner and simpler implementations of tools for SBS, along with better practices.

Questions

Key questions are:

  • How do we characterize notions of homomorphism and isomorphism in sequence enumerations? More...
  • Should we introduce nondeterministic refinements to the framework? More...
  • Is there a natural decomposition (composition) theory for abstractions? More...
  • Is there an advantage to developing the theory using relations instead of functions? More...

In particular, lets develop the theory in the most general sense, with no assumptions of either finiteness or discreteness.

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Early Results

It seems that it is worthwhile to discuss a mathematically simpler object I call a semienumeration before tackling enumerations. It has only a few axioms, and does not associate sequences with values. It isolates the thing that may be most significant in an enumeration: the reduction relation.

Representation theorems abound. Some are potentially quite interesting. If we view each symbol as an operator on sets of sequences, we can transform them problem in to a sigma algebra and investigate properties of its operators (the symbols).