Equation 14 · Part 1 · The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol
Symbol bart_tool
What this part means
the number of tokens.
Its job in the formula
barool is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol bart_tool→Article meaning
Where the article explains it
If every tool schema costs on average tokens and all of them are injected in full on every turn, the maximum number of tools a deployment can nominally offer before it must start pruning or retrieving is
The passage around this formula
Put the three costs together and a deployment question comes into focus: given a fixed context window, how many tools can actually be offered before something has to give? A simple ceiling model makes the trade-off explicit. Let C be the model’s usable context window, the fixed cost of operator instructions, and a reserved allowance for the user’s message and the model’s own answer. If every tool schema costs on average tokens and all of them are injected in full on every turn, the maximum number of tools a deployment can nominally offer before it must start pruning or retrieving is
Learn the underlying idea
A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
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Sources cited in the article section
- [1] Model Context Protocol Specification (2025-06-18) ↗
- [11] Efficient Memory Management for Large Language Model Serving with PagedAttention ↗
These citations provide research context; check each source for the exact claim it supports.