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Time complexity for deterministic string machines

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Nur Cataltepe, Vanessa Kosoy

Formal Languages and Automata Theory · Submitted 9 May 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove sufficient conditions for polynomial runtime guarantees on these, which can help develop complexity constraints on string machines which also encapsulate runtime complexity.

how it is stated · asserted 0.91 read the record →

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arXiv ID2405.06043 (version 2)
Pith ID7KIRJTE4, Pith's permanent record of this paper and its review
CitationNur Cataltepe, Vanessa Kosoy. "Time complexity for deterministic string machines." arXiv:2405.06043 (2024). https://pith.science/paper/7KIRJTE4
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,425 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.56 · human participants 0.02 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.42 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small description length. We thus formalize a compositional language that can construct automata as transformations between certain types of category, representable as string diagrams, which better reflects the description complexity of various automata. We define complexity constraints on this framework by having them operate on categories enriched over filtered sets, and using these constraints, we prove elementary results on the runtime and expressivity of a subset of these transformations which operate deterministically on finite state spaces. These string diagrams, or "string machines," are themselves morphisms in a category, so it is possible for string machines to create other string machines in runtime to model computations which take more than constant memory. We prove sufficient conditions for polynomial runtime guarantees on these, which can help develop complexity constraints on string machines which also encapsulate runtime complexity.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small description length. background 0.97 0.04 0.04 asserted 0.99
s1 We thus formalize a compositional language that can construct automata as transformations between certain types of category, representable as string diagrams, which better reflects the description complexity of various automata. contribution 0.84 0.93 0.11 asserted 0.99
s2 We define complexity constraints on this framework by having them operate on categories enriched over filtered sets, and using these constraints, we prove elementary results on the runtime and expressivity of a subset of these transformations which operate deterministically on finite state spaces. method 0.54 0.95 0.15 asserted 1.00
s3 These string diagrams, or "string machines," are themselves morphisms in a category, so it is possible for string machines to create other string machines in runtime to model computations which take more than constant memory. contribution 0.44 0.47 0.08 hedged possibility 0.51
s4 We prove sufficient conditions for polynomial runtime guarantees on these, which can help develop complexity constraints on string machines which also encapsulate runtime complexity. result 0.86 0.95 0.46 asserted 0.91

What kind of paper the classifier reports this is: theoretical result 0.87 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • figures and tables
  • references and citing sentences
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  • P abstract
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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small description length. We thus formalize a compositional language that can construct automata as transformations between certain types of category, representable as string diagrams, which better reflects the description complexity of various automata. We define complexity constraints on this framework by having them operate on categories enriched over filtered sets, and using these constraints, we prove elementary results on the runtime and expressivity of a subset of these transformations which operate deterministically on finite state spaces. These string diagrams, or "string machines," are themselves morphisms in a category, so it is possible for string machines to create other string machines in runtime to model computations which take more than constant memory. We prove sufficient conditions for polynomial runtime guarantees on these, which can help develop complexity constraints on string machines which also encapsulate runtime complexity.

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