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History-deterministic Vector Addition Systems

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Sougata Bose, David Purser, Patrick Totzke

Formal Languages and Automata Theory · Submitted 3 May 2023

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

The authors' main claim Our results show that the history-deterministic (HD) VASS sit strictly between deterministic and non-deterministic VASS regardless of the number of counters.

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arXiv ID2305.01981 (version 2)
Pith IDI6JB2YTP, Pith's permanent record of this paper and its review
CitationDavid Purser, Patrick Totzke, Sougata Bose. "History-deterministic Vector Addition Systems." arXiv:2305.01981 (2023). https://pith.science/paper/I6JB2YTP
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,142 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.79 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.42 · compares with prior results 0.78 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We consider history-determinism, a restricted form of non-determinism, for Vector Addition Systems with States (VASS) when used as acceptors to recognise languages of finite words. History-determinism requires that the non-deterministic choices can be resolved on-the-fly; based on the past and without jeopardising acceptance of any possible continuation of the input word. Our results show that the history-deterministic (HD) VASS sit strictly between deterministic and non-deterministic VASS regardless of the number of counters. We compare the relative expressiveness of HD systems, and closure-properties of the induced language classes, with coverability and reachability semantics, and with and without $\varepsilon$-labelled transitions. Whereas in dimension 1, inclusion and regularity remain decidable, from dimension two onwards, HD-VASS with suitable resolver strategies, are essentially able to simulate 2-counter Minsky machines, leading to several undecidability results: It is undecidable whether a VASS is history-deterministic, or if a language equivalent history-deterministic VASS exists. Checking language inclusion between history-deterministic 2-VASS is also undecidable.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider history-determinism, a restricted form of non-determinism, for Vector Addition Systems with States (VASS) when used as acceptors to recognise languages of finite words. background 0.52 0.46 0.05 asserted 0.51
s1 History-determinism requires that the non-deterministic choices can be resolved on-the-fly; based on the past and without jeopardising acceptance of any possible continuation of the input word. background 1.00 0.07 0.04 asserted 1.00
s2 Our results show that the history-deterministic (HD) VASS sit strictly between deterministic and non-deterministic VASS regardless of the number of counters. result 1.00 0.94 0.72 asserted 1.00
s3 We compare the relative expressiveness of HD systems, and closure-properties of the induced language classes, with coverability and reachability semantics, and with and without $\varepsilon$-labelled transitions. contribution 0.96 0.84 0.06 asserted 0.66
s4 Whereas in dimension 1, inclusion and regularity remain decidable, from dimension two onwards, HD-VASS with suitable resolver strategies, are essentially able to simulate 2-counter Minsky machines, leading to several undecidability results: It is undecidable whether a VASS is history-deterministic, or if a language equivalent history-deterministic VASS exists. result 0.99 0.88 0.28 asserted 0.99
s5 Checking language inclusion between history-deterministic 2-VASS is also undecidable. result 1.00 0.87 0.11 asserted 1.00

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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

We consider history-determinism, a restricted form of non-determinism, for Vector Addition Systems with States (VASS) when used as acceptors to recognise languages of finite words. History-determinism requires that the non-deterministic choices can be resolved on-the-fly; based on the past and without jeopardising acceptance of any possible continuation of the input word. Our results show that the history-deterministic (HD) VASS sit strictly between deterministic and non-deterministic VASS regardless of the number of counters. We compare the relative expressiveness of HD systems, and closure-properties of the induced language classes, with coverability and reachability semantics, and with and without $\varepsilon$-labelled transitions. Whereas in dimension 1, inclusion and regularity remain decidable, from dimension two onwards, HD-VASS with suitable resolver strategies, are essentially able to simulate 2-counter Minsky machines, leading to several undecidability results: It is undecidable whether a VASS is history-deterministic, or if a language equivalent history-deterministic VASS exists. Checking language inclusion between history-deterministic 2-VASS is also undecidable.

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