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framework:algebraic-structure-theory-of-sequential-machinesAlgebraic Structure Theory of Sequential Machines
Hartmanis & Stearns framework for machine behavior; relevant to formalizing regulators as input-output systems.
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- Poset with join and meet operations satisfying associativity, commutativity, idempotency, and absorption laws.
- The actual computational operations a model performs, which the paper argues need not mirror representational structure
- The definition of 'architecture' in computing as the structural design of systems, dating to 1960s mainframes, central to information architecture.
- Theoretical construct establishing classical demarcation between machine and environment via input/output channels.
- Language model reasoning tasks with sequential geometry used in experiments.
- A most general system of mathematical structures arising from the nature of space, which has degrees of life.
- Fundamental mathematical tool; poset-as-category provides simple instances of categorical notions like products and adjunctions.
- The central question of whether representational geometry implies corresponding computational structure