Axiomatizations and conservation results for fragments of bounded arithmetic

1990 ◽  
pp. 57-84 ◽  
Author(s):  
Samuel R. Buss
Keyword(s):  
Bounded Arithmetic

A note on the Σ1collection scheme and fragments of bounded arithmetic

2010 ◽  
Vol 56 (2) ◽  
pp. 126-130
Author(s):  
Zofia Adamowicz ◽  
Leszek Aleksander Kołodziejczyk
Keyword(s):  
Bounded Arithmetic

scholarly journals FRAGMENTS OF APPROXIMATE COUNTING

2014 ◽  
Vol 79 (2) ◽  
pp. 496-525 ◽  
Author(s):  
SAMUEL R. BUSS ◽  
LESZEK ALEKSANDER KOŁODZIEJCZYK ◽  
NEIL THAPEN
Keyword(s):  
Polynomial Time ◽  
Open Problem ◽  
Bounded Arithmetic ◽  
Pigeonhole Principle ◽  
Approximate Counting ◽  
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AbstractWe study the long-standing open problem of giving $\forall {\rm{\Sigma }}_1^b$ separations for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeřábek’s theories for approximate counting and their subtheories. We show that the $\forall {\rm{\Sigma }}_1^b$ Herbrandized ordering principle is unprovable in a fragment of bounded arithmetic that includes the injective weak pigeonhole principle for polynomial time functions, and also in a fragment that includes the surjective weak pigeonhole principle for FPNP functions. We further give new propositional translations, in terms of random resolution refutations, for the consequences of $T_2^1$ augmented with the surjective weak pigeonhole principle for polynomial time functions.

scholarly journals Automorphisms of models of bounded arithmetic

2006 ◽  
Vol 192 (1) ◽  
pp. 37-65 ◽  
Author(s):  
Ali Enayat
Keyword(s):  
Bounded Arithmetic

Efficient BDDs for bounded arithmetic constraints

2005 ◽  
Vol 8 (1) ◽  
pp. 26-36 ◽  
Author(s):  
Constantinos Bartzis ◽  
Tevfik Bultan
Keyword(s):  
Bounded Arithmetic

Forcing on Bounded Arithmetic

1996 ◽  
pp. 120-138 ◽  
Author(s):  
Gaisi Takeuti ◽  
Masahiro Yasumoto
Keyword(s):  
Bounded Arithmetic
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