---
res:
bibo_abstract:
- 'Abstract. Dynamic programs, or fixpoint iteration schemes, are useful for solving
many problems on state spaces, including model checking on Kripke structures (“verification”),
computing shortest paths on weighted graphs (“optimization”), computing the value
of games played on game graphs (“control”). For Kripke structures, a rich fixpoint
theory is available in the form of the µ-calculus. Yet few connections have been
made between different interpretations of fixpoint algorithms. We study the question
of when a particular fixpoint iteration scheme ϕ for verifying an ω-regular property
Ψ on a Kripke structure can be used also for solving a two-player game on a game
graph with winning objective Ψ. We provide a sufficient and necessary criterion
for the answer to be affirmative in the form of an extremal-model theorem for
games: under a game interpretation, the dynamic program ϕ solves the game with
objective Ψ if and only if both (1) under an existential interpretation on Kripke
structures, ϕ is equivalent to ∃Ψ, and (2) under a universal interpretation on
Kripke structures, ϕ is equivalent to ∀Ψ. In other words, ϕ is correct on all
two-player game graphs iff it is correct on all extremal game graphs, where one
or the other player has no choice of moves. The theorem generalizes to quantitative
interpretations, where it connects two-player games with costs to weighted graphs.
While the standard translations from ω-regular properties to the µ-calculus violate
(1) or (2), we give a translation that satisfies both conditions. Our construction,
therefore, yields fixpoint iteration schemes that can be uniformly applied on
Kripke structures, weighted graphs, game graphs, and game graphs with costs, in
order to meet or optimize a given ω-regular objective.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Luca
foaf_name: de Alfaro, Luca
foaf_surname: De Alfaro
- foaf_Person:
foaf_givenName: Thomas A
foaf_name: Thomas Henzinger
foaf_surname: Henzinger
foaf_workInfoHomepage: http://www.librecat.org/personId=40876CD8-F248-11E8-B48F-1D18A9856A87
orcid: 0000−0002−2985−7724
- foaf_Person:
foaf_givenName: Ritankar
foaf_name: Majumdar, Ritankar S
foaf_surname: Majumdar
bibo_doi: 10.1109/LICS.2001.932504
dct_date: 2001^xs_gYear
dct_publisher: IEEE@
dct_title: 'From verification to control: dynamic programs for omega-regular objectives@'
...