History Determinism vs. Good for Gameness in Quantitative Automata

  title={History Determinism vs. Good for Gameness in Quantitative Automata},
  author={Udi Boker and Karoliina Lehtinen},
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… 
4 Citations

Figures from this paper

Token Games and History-Deterministic Quantitative-Automata
A nondeterministic 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,
Between Deterministic and Nondeterministic Quantitative Automata
The possible generalization of such notions from Boolean to quantitative automata is analyzed, and it is suggested that it depends on the following key characteristics of the considered notion N– whether it is syntactic or semantic, and if semantic,Whether it is word-based or language-based.
Good-for-games $\omega$-Pushdown Automata
These are automata whose nondeterminism can be resolved based on the input processed so far and it is shown that solving infinite games with winning conditions specified by ω-GFG-PDA is EXPTIME-complete.
On the size of good-for-games Rabin automata and its link with the memory in Muller games
It is established that good-for-games Rabin automata that recognise a Muller language are exactly of the same size as the minimal memory required for winning Muller games that have this language as their winning condition, thus proving as a consequence that chromatic memory for winning a Muller game can be exponentially larger than unconstrained memory.


Good for Games Automata: From Nondeterminism to Alternation
It is shown that alternating G FG automata are as expressive as deterministic automata with the same acceptance conditions and indices, and that determinizing Buchi and co-Buchi alternating GFG automata involves a $2^{\Theta(n)}$ state blow-up.
Solving Games Without Determinization
The main insight is that a nondeterministic automaton is good for solving games if it fairly simulates the equivalent deterministicAutomata are constructed that omit the determinization step in game solving and reactive synthesis.
Nondeterminism in the Presence of a Diverse or Unknown Future
It is shown that GFT=GFG⊃DBP, and described a determinization construction for GFG automata, which shows the possible succinctness of GFG and GFT automata compared to deterministic automata.
Alternating Weighted Automata
It is shown that alternation brings more expressive power than nondeterminism for limit average and discounted sum, and the expressive power of the various classes of alternating and nondeterministic weighted automata over infinite words is compared.
Discounted-Sum Automata with Multiple Discount Factors
Tidy N MDAs are as expressive as deterministic integral NMDAs with an arbitrary choice of discount factors, and some of their special cases are NMD as in which the discount factor depends on the action or on the elapsed time.
Better Quality in Synthesis through Quantitative Objectives
It is shown how automata with lexicographic mean-payoff conditions can be used to express many interesting quantitative properties for reactive systems, and how quantitative properties to measure the "goodness" of an implementation are used.
The Theory of Stabilisation Monoids and Regular Cost Functions
The notion of regular cost functions is introduced: a quantitative extension to the standard theory of regular languages, and a suitable notion of recognisability by stabilisation monoids is provided, and closure and decidability results are provided.
Synthesis from Weighted Specifications with Partial Domains over Finite Words
An infinite game framework is developed to solve the corresponding synthesis problems, namely the class of (weighted) critical prefix games and the resulting objectives are not regular in general.
Reasoning about online algorithms with weighted automata
An automata-theoretic approach is described that is able to solve problems about the competitive ratio of online algorithms, and the memory they require, by reducing them to questions about determinization and approximated determinization of weighted automata.