Unboundedness Problems for Machines with Reversal-Bounded Counters
Bibliographic record
Abstract
Abstract We consider a general class of decision problems concerning formal languages, called “(one-dimensional) unboundedness predicates”, for automata that feature reversal-bounded counters (RBCA). We show that each problem in this class reduces—non-deterministically in polynomial time—to the same problem for just finite automata. We also show an analogous reduction for automata that have access to both a pushdown stack and reversal-bounded counters (PRBCA). This allows us to answer several open questions: For example, we show that it is $$\textsf{coNP}$$ coNP -complete to decide whether a given (P)RBCA language L is bounded, meaning whether there exist words $$w_1,\ldots ,w_n$$ w 1 , … , w n with $$L\subseteq w_1^*\cdots w_n^*$$ L ⊆ w 1 ∗ ⋯ w n ∗ . For PRBCA, even decidability was open. Our methods also show that there is no language of a (P)RBCA of intermediate growth. This means, the number of words of each length grows either polynomially or exponentially. Part of our proof is likely of independent interest: We show that one can translate an RBCA into a machine with $$\mathbb {Z}$$ Z -counters in logarithmic space, while preserving the accepted language.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.005 | 0.010 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".