A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct

Guha, Shibashis; Jecker, Ismaël; Lehtinen, Karoliina; Zimmermann, Martin

doi:10.48550/arxiv.2105.02611

Cited by 3 publications

(2 citation statements)

References 31 publications

(59 reference statements)

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“…The local best value (or t-threshold) synthesis problem of a function given by deterministic (or even history-deterministic nondeterministic) automata and the problem of whether a nondeterministic automaton is (t-threshold) history deterministic reduce to each other. The relationship between good-enough synthesis [1] and history determinism was noted for visibly pushdown automata in [13]; a similar reduction in [12] reduces the approximative local bestvalue synthesis of deterministic quantitative automata over finite words by finite transducers to the notion of r-regret determinisability, that is, whether a nondeterministic automaton is close enough to a deterministic automaton obtained by pruning its product with a finite memory. Our reductions are in the same spirit, but relate the synthesis problem to history determinism rather than determinisability, and obtain a two-way correspondence for all history-deterministic nondeterministic quantitative automata.…”

Section: :16 History Determinism Vs Good For Gamenessmentioning

confidence: 93%

History Determinism vs. Good for Gameness in Quantitative Automata

Boker¹,

Lehtinen²

2021

Preprint

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Automata models between determinism and nondeterminism/alternations can retain some of the algorithmic properties of deterministic automata while enjoying some of the expressiveness and succinctness of nondeterminism. We study three closely related such models -history determinism, good for gameness and determinisability by pruning -on quantitative automata.While in the Boolean setting, history determinism and good for gameness coincide, we show that this is no longer the case in the quantitative setting: good for gameness is broader than history determinism, and coincides with a relaxed version of it, defined with respect to thresholds. We further identify criteria in which history determinism, which is generally broader than determinisability by pruning, coincides with it, which we then apply to typical quantitative automata types.As a key application of good for games and history deterministic automata is synthesis, we clarify the relationship between the two notions and various quantitative synthesis problems. We show that good-for-games automata are central for "global" (classical) synthesis, while "local" (good-enough) synthesis reduces to deciding whether a nondeterministic automaton is history deterministic.

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Section: :16 History Determinism Vs Good For Gamenessmentioning

confidence: 93%

History Determinism vs. Good for Gameness in Quantitative Automata

Boker¹,

Lehtinen²

2021

Preprint

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“…History determinism lies in between determinism and nondeterminism, enjoying in some aspects the best of both worlds: HD automata are, like deterministic ones, useful for solving games and reactive synthesis [16,11,17,18,19,12,15,7], while they can sometimes be more expressive and/or succinct. For example, HD coBüchi and LimInf automata can be exponentially more succinct than deterministic ones [20], and HD pushdown automata are both more expressive and at least exponentially more succinct than deterministic pushdown automata [21,15]. Notice that in the (ω-)regular setting, history determinism coincides with good for gameness [6], while in the quantitative setting it is stronger than good-for-gameness [7].…”

Section: Introductionmentioning

confidence: 99%

Token Games and History-Deterministic Quantitative-Automata

Boker¹,

Lehtinen²

2021

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A nondeterministic (quantitative) automaton is history deterministic if its nondeterminism can be resolved by only considering the prefix of the word read so far. Due to their good compositional properties, history deterministic automata are useful in solving games and synthesis problems. Deciding whether or not a given nondeterministic automaton is history deterministic (the HDness problem) is generally a difficult task, which might involve an exponential procedure, or even be undecidable, for example for pushdown automata. Token games provide a PTime solution to the HDness problem of Büchi and coBüchi automata, and it is conjectured that 2-token games characterize HDness for all ω-regular automata. We extend token games to the quantitative setting and analyze their potential to help deciding HDness for quantitative automata. In particular, we show that 1-token games characterize HDness for all quantitative (and Boolean) automata on finite words, as well as discounted-sum (DSum) automata on infinite words, and that 2-token games characterize HDness of LimInf and LimSup automata. Using these characterizations, we provide solutions to the HDness problem of Inf and Sup automata on finite words in PTime, for DSum automata on finite and infinite words in NP∩co-NP, for LimSup automata in quasipolynomial time, and for LimInf automata in exponential time, where the latter two are only polynomial for automata with a fixed number of weights.

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When a Little Nondeterminism Goes a Long Way

Boker

Lehtinen

2023

ACM SIGLOG News

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History-deterministic automata are an intermediate automata model, in between deterministic and nondeterministic ones. An automaton is history-deterministic if its nondeterminism can be resolved on-the-fly, by only taking into account the prefix of the word read so far. This restricted form of nondeterminism yields a class of automata that retains some of the algorithmic properties of deterministic automata, while also enjoying some of the power of nondeterminism. History-determinism has received a lot of attention in the past few years and this article surveys some of the recent developments on the topic. It aims to showcase some of the key constructions and techniques involved in this line of research, while remaining fairly informal. We begin with a roughly chronological overview of research on history-determinism, intended as a quick reference to some of the main results on the subject. We then move onto a more detailed discussion of what are, in our view, the key aspects of history-determinism, highlighting throughout questions that remain open. Like any survey written on a topic that is actively worked on, this article aspires to be out-of-date as soon as it is published. We hope that it will remain useful as a gentle, if incomplete, introduction to the topic.

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A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct

Cited by 3 publications

References 31 publications

History Determinism vs. Good for Gameness in Quantitative Automata

History Determinism vs. Good for Gameness in Quantitative Automata

Token Games and History-Deterministic Quantitative-Automata

When a Little Nondeterminism Goes a Long Way

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