223 research outputs found
Parity and Streett Games with Costs
We consider two-player games played on finite graphs equipped with costs on
edges and introduce two winning conditions, cost-parity and cost-Streett, which
require bounds on the cost between requests and their responses. Both
conditions generalize the corresponding classical omega-regular conditions and
the corresponding finitary conditions. For parity games with costs we show that
the first player has positional winning strategies and that determining the
winner lies in NP and coNP. For Streett games with costs we show that the first
player has finite-state winning strategies and that determining the winner is
EXPTIME-complete. The second player might need infinite memory in both games.
Both types of games with costs can be solved by solving linearly many instances
of their classical variants.Comment: A preliminary version of this work appeared in FSTTCS 2012 under the
name "Cost-parity and Cost-Streett Games". The research leading to these
results has received funding from the European Union's Seventh Framework
Programme (FP7/2007-2013) under grant agreements 259454 (GALE) and 239850
(SOSNA
Can Nondeterminism Help Complementation?
Complementation and determinization are two fundamental notions in automata
theory. The close relationship between the two has been well observed in the
literature. In the case of nondeterministic finite automata on finite words
(NFA), complementation and determinization have the same state complexity,
namely Theta(2^n) where n is the state size. The same similarity between
determinization and complementation was found for Buchi automata, where both
operations were shown to have 2^\Theta(n lg n) state complexity. An intriguing
question is whether there exists a type of omega-automata whose determinization
is considerably harder than its complementation. In this paper, we show that
for all common types of omega-automata, the determinization problem has the
same state complexity as the corresponding complementation problem at the
granularity of 2^\Theta(.).Comment: In Proceedings GandALF 2012, arXiv:1210.202
Computer aided synthesis: a game theoretic approach
In this invited contribution, we propose a comprehensive introduction to game
theory applied in computer aided synthesis. In this context, we give some
classical results on two-player zero-sum games and then on multi-player non
zero-sum games. The simple case of one-player games is strongly related to
automata theory on infinite words. All along the article, we focus on general
approaches to solve the studied problems, and we provide several illustrative
examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language
Theory" (DLT 2017
Parameterized Linear Temporal Logics Meet Costs: Still not Costlier than LTL
We continue the investigation of parameterized extensions of Linear Temporal
Logic (LTL) that retain the attractive algorithmic properties of LTL: a
polynomial space model checking algorithm and a doubly-exponential time
algorithm for solving games. Alur et al. and Kupferman et al. showed that this
is the case for Parametric LTL (PLTL) and PROMPT-LTL respectively, which have
temporal operators equipped with variables that bound their scope in time.
Later, this was also shown to be true for Parametric LDL (PLDL), which extends
PLTL to be able to express all omega-regular properties.
Here, we generalize PLTL to systems with costs, i.e., we do not bound the
scope of operators in time, but bound the scope in terms of the cost
accumulated during time. Again, we show that model checking and solving games
for specifications in PLTL with costs is not harder than the corresponding
problems for LTL. Finally, we discuss PLDL with costs and extensions to
multiple cost functions.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Improved Algorithms for Parity and Streett objectives
The computation of the winning set for parity objectives and for Streett
objectives in graphs as well as in game graphs are central problems in
computer-aided verification, with application to the verification of closed
systems with strong fairness conditions, the verification of open systems,
checking interface compatibility, well-formedness of specifications, and the
synthesis of reactive systems. We show how to compute the winning set on
vertices for (1) parity-3 (aka one-pair Streett) objectives in game graphs in
time and for (2) k-pair Streett objectives in graphs in time
. For both problems this gives faster algorithms for dense
graphs and represents the first improvement in asymptotic running time in 15
years
Mixing Probabilistic and non-Probabilistic Objectives in Markov Decision Processes
In this paper, we consider algorithms to decide the existence of strategies
in MDPs for Boolean combinations of objectives. These objectives are
omega-regular properties that need to be enforced either surely, almost surely,
existentially, or with non-zero probability. In this setting, relevant
strategies are randomized infinite memory strategies: both infinite memory and
randomization may be needed to play optimally. We provide algorithms to solve
the general case of Boolean combinations and we also investigate relevant
subcases. We further report on complexity bounds for these problems.Comment: Paper accepted to LICS 2020 - Full versio
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