252 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
'Our land abounds in nature's gifts': Commodity frontiers, Australian capitalism, and socioecological crisis
This thesis presents a history of the origins of capitalism on the continent of Australia. It begins from a contemporary conjuncture riven with socioecological crises that demand theoretical and historical explanation â a conjuncture of mass extinction, of collapsing ecosystems, of accelerating climatic change. From this vantage-point we look to theorise and historicise capitalism in Australia. Animating this history is our central research question: how have âcommodity frontiersâ shaped the socioecology of Australian capitalism? This question brings the tools of historical materialism â especially in its eco-socialist and world-ecological forms â to bear on the historical origins of Australian capitalism, enabling an understanding of the production of nature and socioecological crisis in Australia. The argument begins from a definition of capitalism as a historically specific totality of socioecological relations: internally related processes of cheap nature, state formation, racialization, and gendered difference driven forward by the structuring power of the value form. These relations violently displaced extant Indigenous socioecologies, spreading across the landscape of Australia via the vehicle of âcommodity frontiers.â The thesis traces empirically the process of invasion, and the production of cheap nature through an incorporated comparison of three frontiers â wool, coal, and sugar. In exploring the internal relations of these frontiers through space and time we find them bound within the same totality, defined by dialectics of appropriation and exploitation, of crisis and expansion, of cheapness and of great cost. Put simply, the thesis grapples with the political and analytical challenge of the Capitalocene, and looks to contribute to its undoing through a retelling of the history of the invasion of this continent, and an apprehension of the nature of capitalism
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
NP-Hardness of Approximating Meta-Complexity: A Cryptographic Approach
It is a long-standing open problem whether the Minimum Circuit Size Problem () and related meta-complexity problems are NP-complete. Even for the rare cases where the NP-hardness of meta-complexity problems are known, we only know very weak hardness of approximation.
In this work, we prove NP-hardness of approximating meta-complexity with nearly-optimal approximation gaps. Our key idea is to use *cryptographic constructions* in our reductions, where the security of the cryptographic construction implies the correctness of the reduction. We present both conditional and unconditional hardness of approximation results as follows.
Assuming subexponentially-secure witness encryption exists, we prove essentially optimal NP-hardness of approximating conditional time-bounded Kolmogorov complexity () in the regime where . Previously, the best hardness of approximation known was a factor and only in the sublinear regime ().
Unconditionally, we show near-optimal NP-hardness of approximation for the Minimum Oracle Circuit Size Problem (MOCSP), where Yes instances have circuit complexity at most , and No instances are essentially as hard as random truth tables. Our reduction builds on a witness encryption construction proposed by Garg, Gentry, Sahai, and Waters (STOC\u2713). Previously, it was unknown whether it is NP-hard to distinguish between oracle circuit complexity versus .
Finally, we define a multi-valued version of , called , and show that w.p. over a random oracle , is NP-hard to approximate under quasi-polynomial-time reductions with oracle access. Intriguingly, this result follows almost directly from the security of Micali\u27s CS proofs (Micali, SICOMP\u2700).
In conclusion, we give three results convincingly demonstrating the power of cryptographic techniques in proving NP-hardness of approximating meta-complexity
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
Towards Optimal Depth-Reductions for Algebraic Formulas
Classical results of Brent, Kuck and Maruyama (IEEE Trans. Computers 1973)
and Brent (JACM 1974) show that any algebraic formula of size s can be
converted to one of depth O(log s) with only a polynomial blow-up in size. In
this paper, we consider a fine-grained version of this result depending on the
degree of the polynomial computed by the algebraic formula. Given a homogeneous
algebraic formula of size s computing a polynomial P of degree d, we show that
P can also be computed by an (unbounded fan-in) algebraic formula of depth
O(log d) and size poly(s). Our proof shows that this result also holds in the
highly restricted setting of monotone, non-commutative algebraic formulas. This
improves on previous results in the regime when d is small (i.e., d<<s). In
particular, for the setting of d=O(log s), along with a result of Raz (STOC
2010, JACM 2013), our result implies the same depth reduction even for
inhomogeneous formulas. This is particularly interesting in light of recent
algebraic formula lower bounds, which work precisely in this ``low-degree" and
``low-depth" setting. We also show that these results cannot be improved in the
monotone setting, even for commutative formulas
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