Reactive Synthesis Without Regret

Two-player zero-sum games of infinite duration and their quantitative versions are used in verification to model the interaction between a controller (Eve) and its environment (Adam). The question usually addressed is that of the existence (and computability) of a strategy for Eve that can maximize her payoff against any strategy of Adam. In this work, we are interested in strategies of Eve that minimize her regret, i.e. strategies that minimize the difference between her actual payoff and the payoff she could have achieved if she had known the strategy of Adam in advance. We give algorithms to compute the strategies of Eve that ensure minimal regret against an adversary whose choice of strategy is (i) unrestricted, (ii) limited to positional strategies, or (iii) limited to word strategies, and show that the two last cases have natural modelling applications. We also show that our notion of regret minimization in which Adam is limited to word strategies generalizes the notion of good for games introduced by Henzinger and Piterman, and is related to the notion of determinization by pruning due to Aminof, Kupferman and Lampert

Begin Now

In the following love poem all the words are in alphabetical order. I am indebted to the much more extensive, if much less sensible and cyntactical, Legendary, Lexical, Loquacious Love by Eve Rhymer. Her work contains all the words from a romance novel, alphabetized into 25 chapters (no X). A more sensible and very impressive work of this sort is the last chapter of Walter Abish\u27s novel Alphabetical Africa, a list of alphabetized two-word phrases that recapitulate the novel

Letter from John Muir to Louie, Wanda & Helen, 1899 Jun 16.

[letterhead]June 16 1899Dear Louie Wanda & Helen:.I wrote two days ago & I suppose you will get this at the same time as the other. We had the Governor at dinner & a society affair afterward that looked queer in the wilderness. This eve we are to have a reception at the Governors & tomorrow we sail for Yakutat Bay Thence to Prince William Sound & Cooks Inlet etc. We were at the Hot Springs yesterday 15 miles from here amid lovely scenery. The Topeka arrived last eve & sails in an hour or so. I met Professor Moses & his wife on the wharf & then a lot of Berkeley people besides. Then the Raymond agent who introduced a lot of people to whom I lectured in the street The thing was like a revival meeting. The weather is wondrous fine & all goes well I regret not having a letter forwarded here. as I long for a word of your welfare. Remember me to Maggie I hope she stands the hot weather.Ever Yours Heaven keep you, darlingsJohn Mui

Non-Zero Sum Games for Reactive Synthesis

In this invited contribution, we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications. These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.Comment: LATA'16 invited pape

Relating timed and register automata

Timed automata and register automata are well-known models of computation over timed and data words respectively. The former has clocks that allow to test the lapse of time between two events, whilst the latter includes registers that can store data values for later comparison. Although these two models behave in appearance differently, several decision problems have the same (un)decidability and complexity results for both models. As a prominent example, emptiness is decidable for alternating automata with one clock or register, both with non-primitive recursive complexity. This is not by chance. This work confirms that there is indeed a tight relationship between the two models. We show that a run of a timed automaton can be simulated by a register automaton, and conversely that a run of a register automaton can be simulated by a timed automaton. Our results allow to transfer complexity and decidability results back and forth between these two kinds of models. We justify the usefulness of these reductions by obtaining new results on register automata.Comment: In Proceedings EXPRESS'10, arXiv:1011.601

Analyzing Timed Systems Using Tree Automata

Timed systems, such as timed automata, are usually analyzed using their operational semantics on timed words. The classical region abstraction for timed automata reduces them to (untimed) finite state automata with the same time-abstract properties, such as state reachability. We propose a new technique to analyze such timed systems using finite tree automata instead of finite word automata. The main idea is to consider timed behaviors as graphs with matching edges capturing timing constraints. When a family of graphs has bounded tree-width, they can be interpreted in trees and MSO-definable properties of such graphs can be checked using tree automata. The technique is quite general and applies to many timed systems. In this paper, as an example, we develop the technique on timed pushdown systems, which have recently received considerable attention. Further, we also demonstrate how we can use it on timed automata and timed multi-stack pushdown systems (with boundedness restrictions)