P.D. Lincoln, J.C. Mitchell, and A. Scedrov. Linear logic proof games and optimization. Preliminary report, January 1996. Available by anonymous ftp from ftp.cis.upenn.edu as pub/papers/scedrov/approx.[dvi,ps].Z. See pub/papers/TableOfContents. Home/Search Document Not in Database Summary Related Articles Check |
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Linear Logic Proof Games and Optimization (Extended Abstract) - Lincoln, al. Self-citation (Lincoln) (Correct)
....of linear logic allow us to restrict provable mall sequents to those that contain only formulas of depth at most 2. Theorems 7.3, 7.5, and 7.6 have analogs in the case in which the game is played against a universal opponent, but that case must be omitted here. The reader is referred to [23]. Our results also have implications for proof search heuristics in linear logic. This is discussed in [24] Acknowledgements: We would like to thank Madhu Sudan for directing us to [10, 9] and Sanjeev Arora and Joan Feigenbaum for their informative conversations and email correspondence and for ....
P.D. Lincoln, J.C. Mitchell, and A. Scedrov. Linear logic proof games and optimization. Preliminary report, January 1996. Available by anonymous ftp from ftp.cis.upenn.edu as pub/papers/scedrov/approx.[dvi,ps].Z. See pub/papers/TableOfContents.
The Complexity of Local Proof Search in Linear Logic - Lincoln, Mitchell, Scedrov (1996) Self-citation (Lincoln Mitchell Scedrov Proof) (Correct)
.... ability to reflect computational states, events, and resources [11, 27, 28] Several notions of game semantics for linear logic are investigated in [6, 1, 2, 13, 17, 15, 9] Connections between linear logic proof search and probabilistic games considered in complexity theory are investigated in [20, 21, 22]. In particular, linear logic proof search may also be seen as a game. This game, the linear logic proof game, is played on linear logic formulas, and its moves are instances of inference rules of linear logic. There are two players, called proponent and opponent, and a separate verifier. ....
....by NSF Grant CCR 94 00907, by ONR Grant N00014 92J 1916, and by a Centennial Research Fellowship from the American Mathematical Society. 1 direction of proponent s evidence in a way that makes it impossible for proponent to obtain a formal proof. Several versions of this game are discussed in [21, 22], each with a numeric score that reflects the number of certain preferred axioms used in a complete or partial formal proof. The capabilities of the players may differ. While proponent is always omnipotent, in some versions of the game opponent s decisions are based only on a fair coin toss. Two ....
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P.D. Lincoln, J.C. Mitchell, and A. Scedrov. Linear logic proof games and optimization. Preliminary report, January 1996. Available by anonymous ftp from ftp.cis.upenn.edu as pub/papers/scedrov/approx.[dvi,ps].Z. See pub/papers/TableOfContents.
Optimization Complexity of Linear Logic Proof Games - Lincoln, Mitchell, Scedrov (1 citation) Self-citation (Lincoln Mitchell Scedrov Proof) (Correct)
....the best score possible. Let us first consider a simple version of the game against a randomized opponent, which can be described as an avg max game played on mall sequents. The game may also be presented as a board game with tiles, where each tile is marked by a linear logic inference rule [24, 26]. Proponent chooses the inference rule to be applied. In the case Omega , proponent chooses a partition and requires both associated expressions to be evaluated. In the case Phi , proponent chooses which of the two expressions will be evaluated. In the case , opponent chooses by a fair coin ....
....[j Delta j] defined in Section 7.1 is computed with A = The second part follows from Theorem 5.2 by the same encoding. Theorems 7.3, 3.5, and 7.8 have analogs in the case in which the game is played against a universal opponent, but that case is omitted here. The reader is referred to [26]. 8 Lower bounds for local proof heuristics We have shown in the previous sections that the optimal score functions ; ae and the corresponding optimal strategies for proponent are pspace hard to approximate on mall formulas and np hard to approximate on mll formulas. Some of these properties ....
P.D. Lincoln, J.C. Mitchell, and A. Scedrov. Linear logic proof games and optimization. Preliminary report, January 1996. Available by anonymous ftp from ftp.cis.upenn.edu as pub/papers/scedrov/approx.[dvi,ps].Z. See pub/papers/TableOfContents.
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