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Perfect Half Space Games Thomas Colcombet, Marcin Jurdzi nski, - PowerPoint PPT Presentation

Jul 09, 2023 •42 likes •522 views

Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games Perfect Half Space Games Thomas Colcombet, Marcin Jurdzi nski, Ranko Lazi c, and Sylvain Schmitz LSV, ENS Paris-Saclay & CNRS & Inria LICS 2017,

Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games Perfect Half Space Games Thomas Colcombet, Marcin Jurdzi´ nski, Ranko Lazi´ c, and Sylvain Schmitz LSV, ENS Paris-Saclay & CNRS & Inria LICS 2017, June 23rd, 2017 1/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games What to do this week-end? Uncontrolled events Maximal dry temperature Discrete resources as a parity objective Uncontrolled events as a two-players game Discrete resources 6 o M M´ yvatn as a multi-energy objective 0 0 10 o H Hr´ utafj¨ ordur 1 1 (− 1,0 ) (− 1,0 ) (− 2, − 1 ) (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 0 4 o Vatnaj¨ okull V 0 0 Reykjavik R 9 o 13 o L Landmannalaugar (− 1,0 ) 2 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 1 12 o Th´ orsm¨ ork T 2/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games What to do this week-end? Uncontrolled events Maximal dry temperature Discrete resources as a parity objective Uncontrolled events as a two-players game Discrete resources 6 o M M´ yvatn as a multi-energy objective 0 0 10 o H Hr´ utafj¨ ordur 1 1 (− 1,0 ) (− 1,0 ) (− 2, − 1 ) (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 0 4 o Vatnaj¨ okull V 0 0 Reykjavik R 9 o 13 o L Landmannalaugar (− 1,0 ) 2 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 1 12 o Th´ orsm¨ ork T 2/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games What to do this week-end? Uncontrolled events Maximal dry temperature Discrete resources as a parity objective Uncontrolled events as a two-players game Discrete resources 6 o M M´ yvatn as a multi-energy objective 0 0 10 o H Hr´ utafj¨ ordur 1 1 (− 1,0 ) (− 1,0 ) (− 2, − 1 ) (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 0 4 o Vatnaj¨ okull V 0 0 Reykjavik R 9 o 13 o L Landmannalaugar (− 1,0 ) 2 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 1 12 o Th´ orsm¨ ork T 2/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games What to do this week-end? Uncontrolled events Maximal dry temperature Discrete resources as a parity objective Uncontrolled events as a two-players game Discrete resources 6 o M M´ yvatn as a multi-energy objective 0 0 10 o H Hr´ utafj¨ ordur 1 1 (− 1,0 ) (− 1,0 ) (− 2, − 1 ) (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 0 4 o Vatnaj¨ okull V 0 0 Reykjavik R 9 o 13 o L Landmannalaugar (− 1,0 ) 2 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 1 12 o Th´ orsm¨ ork T 2/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games What to do this week-end? Uncontrolled events Maximal dry temperature Discrete resources as a parity objective Uncontrolled events as a two-players game Discrete resources 6 o M M´ yvatn as a multi-energy objective 0 0 10 o H Hr´ utafj¨ ordur 1 1 (− 1,0 ) (− 1,0 ) (− 2, − 1 ) (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 0 4 o Vatnaj¨ okull V 0 0 Reykjavik R 9 o 13 o L Landmannalaugar (− 1,0 ) 2 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 1 12 o Th´ orsm¨ ork T 2/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games What to do this week-end? Uncontrolled events Maximal dry temperature Discrete resources as a parity objective Uncontrolled events as a two-players game Discrete resources 6 o M M´ yvatn as a multi-energy objective 0 0 10 o H Hr´ utafj¨ ordur 1 1 (− 1,0 ) (− 1,0 ) (− 2, − 1 ) (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 0 4 o Vatnaj¨ okull V 0 0 Reykjavik R 9 o 13 o L Landmannalaugar (− 1,0 ) 2 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 1 12 o Th´ orsm¨ ork T 2/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games What to do this week-end? Uncontrolled events Maximal dry temperature Discrete resources as a parity objective Uncontrolled events as a two-players game Discrete resources 6 o M M´ yvatn as a multi-energy objective 0 0 10 o H Hr´ utafj¨ ordur 1 1 (− 1,0 ) (− 1,0 ) (− 2, − 1 ) (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 0 4 o Vatnaj¨ okull V 0 0 Reykjavik R 9 o 13 o L Landmannalaugar (− 1,0 ) 2 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 1 12 o Th´ orsm¨ ork T 2/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games What to do this week-end? Uncontrolled events Maximal dry temperature Discrete resources as a parity objective Uncontrolled events as a two-players game Discrete resources 6 o M M´ yvatn as a multi-energy objective 0 0 10 o H Hr´ utafj¨ ordur 1 1 (− 1,0 ) (− 1,0 ) (− 2, − 1 ) (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 0 4 o Vatnaj¨ okull V 0 0 Reykjavik R 9 o 13 o L Landmannalaugar (− 1,0 ) 2 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 1 12 o Th´ orsm¨ ork T 2/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games What to do this week-end? Uncontrolled events Maximal dry temperature Discrete resources as a parity objective Uncontrolled events as a two-players game Discrete resources 6 o M M´ yvatn as a multi-energy objective 0 0 10 o H Hr´ utafj¨ ordur 1 1 (− 1,0 ) (− 1,0 ) (− 2, − 1 ) (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 0 4 o Vatnaj¨ okull V 0 0 Reykjavik R 9 o 13 o L Landmannalaugar (− 1,0 ) 2 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 1 12 o Th´ orsm¨ ork T 2/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games What to do this week-end? Uncontrolled events Maximal dry temperature Discrete resources as a parity objective Uncontrolled events as a two-players game Discrete resources 6 o M M´ yvatn as a multi-energy objective 0 0 10 o H Hr´ utafj¨ ordur 1 1 (− 1,0 ) (− 1,0 ) (− 2, − 1 ) (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 0 4 o Vatnaj¨ okull V 0 0 Reykjavik R 9 o 13 o L Landmannalaugar (− 1,0 ) 2 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 1 12 o Th´ orsm¨ ork T 2/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games What to do this week-end? Uncontrolled events Maximal dry temperature Discrete resources as a parity objective Uncontrolled events as a two-players game Discrete resources 6 o M M´ yvatn as a multi-energy objective 0 0 10 o H Hr´ utafj¨ ordur 1 1 (− 1,0 ) (− 1,0 ) (− 2, − 1 ) (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 0 4 o Vatnaj¨ okull V 0 0 Reykjavik R 9 o 13 o L Landmannalaugar (− 1,0 ) 2 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 1 12 o Th´ orsm¨ ork T 2/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games Multi-Dimensional Energy Parity Games M Player 1 wins a play if both 0 H 1 (− 1,0 ) ◮ energy objective: no (− 1,0 ) (− 2, − 1 ) component goes negative (− 1,0 ) (− 1,0 ) ( 0,0 ) 0 V ◮ parity objective: the maximal 0 R L (− 1,0 ) priority is odd 2 (− 4, − 5 ) ( 1,0 ) ( 0,0 ) (− 4, − 3 ) 1 T Example ( 1,0 ) ( 1,0 ) (− 1,0 ) ( 0,0 ) R ( 0,0 ) − − − → R ( 1,0 ) − − − → R ( 2,0 ) − − − − → H ( 1,0 ) − − − → R ( 1,0 ) → ··· 3/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games Multi-Dimensional Energy Parity Games Applications ◮ contractive ( ⊕ ,! ) -Horn linear logic (Kanovich, APAL ’95) ◮ (weak) simulation of finite-state systems by Petri nets (Abdulla et al., Concur ’13) ◮ model-checking Petri nets with a fragment of µ -calculus (Abdulla et al., Concur ’13) ◮ resource-bounded agent temporal logic RB ± ATL ∗ (Alechina et al., RP ’16 & AI ’17) 3/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games Multi-Dimensional Energy Parity Games Complexity lower bound upper bound w. initial credit ∃ initial credit 3/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games Multi-Dimensional Energy Parity Games Complexity lower bound upper bound EXPSPACE TOWER w. initial credit (Lasota, IPL ’09) (Br´ azdil et al., ICALP ’10) coNP coNP ∃ initial credit (Chatterjee et al., FSTTCS ’10) (Chatterjee et al., FSTTCS ’10) 3/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games Multi-Dimensional Energy Parity Games Complexity lower bound upper bound 2-EXP TOWER w. initial credit (Courtois and S., MFCS ’14) (Br´ azdil et al., ICALP ’10) coNP coNP ∃ initial credit (Chatterjee et al., FSTTCS ’10) (Chatterjee et al., FSTTCS ’10) 3/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games Multi-Dimensional Energy Parity Games Complexity lower bound upper bound 2-EXP 2-EXP w. initial credit (Courtois and S., MFCS ’14) (Jurdzi´ nski et al., ICALP ’15) coNP coNP ∃ initial credit (Chatterjee et al., FSTTCS ’10) (Chatterjee et al., FSTTCS ’10) 3/10
Energy Parity Games Extended Energy Games Bounding Games Perfect Half Space Games Multi-Dimensional Energy Parity Games Complexity lower bound upper bound 2-EXP w. initial credit (Courtois and S., MFCS ’14) coNP coNP ∃ initial credit (Chatterjee et al., Concur ’12) (Chatterjee et al., Concur ’12) 3/10

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