Language Acceptors with a Pushdown: Characterizations and Complexity
Bibliographic record
Abstract
We study one-way nondeterministic pushdown automata ([Formula: see text]), optionally with reversal-bounded counters. Finite-turn pushdown automata are pushdown automata with a bound on the number of switches between pushing and popping. We give new characterizations for finite-turn pushdown automata, and for finite-turn pushdown automata augmented with reversal-bounded counters. The first is in terms of multi-tape nondeterministic finite automata ([Formula: see text]), and the second is in terms of multi-tape [Formula: see text] with reversal-bounded counters. We then use the characterizations to determine the complexity of the languages defined by these automata. In particular, we show that languages accepted by finite-turn [Formula: see text] augmented with reversal-bounded counters are in [Formula: see text]. For the non-finite-turn case, the languages are in [Formula: see text] and in [Formula: see text]. We also look at the space complexity of languages accepted by two-way machines. In particular, we show that every language accepted by a two-way [Formula: see text] with reversal-bounded counters that makes a polynomial (resp., exponential) number of input head reversals is in [Formula: see text] (resp., [Formula: see text]). This remains true if the pushdown can flip its contents a bounded number of times.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".