13 research outputs found
Revisiting Weak Simulation for Substochastic Markov Chains
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One Theorem to Rule Them All: A Unified Translation of LTL into {\omega}-Automata
We present a unified translation of LTL formulas into deterministic Rabin
automata, limit-deterministic B\"uchi automata, and nondeterministic B\"uchi
automata. The translations yield automata of asymptotically optimal size
(double or single exponential, respectively). All three translations are
derived from one single Master Theorem of purely logical nature. The Master
Theorem decomposes the language of a formula into a positive boolean
combination of languages that can be translated into {\omega}-automata by
elementary means. In particular, Safra's, ranking, and breakpoint constructions
used in other translations are not needed
Fixed-Dimensional Energy Games are in Pseudo-Polynomial Time
We generalise the hyperplane separation technique (Chatterjee and Velner,
2013) from multi-dimensional mean-payoff to energy games, and achieve an
algorithm for solving the latter whose running time is exponential only in the
dimension, but not in the number of vertices of the game graph. This answers an
open question whether energy games with arbitrary initial credit can be solved
in pseudo-polynomial time for fixed dimensions 3 or larger (Chaloupka, 2013).
It also improves the complexity of solving multi-dimensional energy games with
given initial credit from non-elementary (Br\'azdil, Jan\v{c}ar, and
Ku\v{c}era, 2010) to 2EXPTIME, thus establishing their 2EXPTIME-completeness.Comment: Corrected proof of Lemma 6.2 (thanks to Dmitry Chistikov for spotting
an error in the previous proof