Counting problems in bounded arithmetic

1985 ◽  
pp. 317-340 ◽  
Author(s):  
J. Paris ◽  
A. Wilkie
Keyword(s):  
Bounded Arithmetic ◽  
Counting Problems

Finite automata, real time processes and counting problems in bounded arithmetics

1988 ◽  
Vol 53 (1) ◽  
pp. 243-258 ◽  
Author(s):  
Mirosław Kutyłowski
Keyword(s):  
Real Time ◽  
Finite Automata ◽  
Bounded Arithmetic ◽  
Negative Solution ◽  
Counting Problems

AbstractIn this paper we present a negative solution of counting problems for some classes slightly different from bounded arithmetic (Δ0sets). To get the results we study properties of chains of finite automata.

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 A computational proof of complexity of some restricted counting problems

2011 ◽  
Vol 412 (23) ◽  
pp. 2468-2485 ◽  
Author(s):  
Jin-Yi Cai ◽  
Pinyan Lu ◽  
Mingji Xia
Keyword(s):  
Counting Problems

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 ◽  
Image Position

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.

Media Clips: Boulder Lottery; The Probability of Slot Machines

2013 ◽  
Vol 107 (3) ◽  
pp. 172-175
Author(s):  
Kristy B. McGowan ◽  
Nathan J. Lowe Spicer
Keyword(s):  
Slot Machines ◽  
Counting Problems ◽  
State Lottery ◽  
The Media

Students analyze items from the media to answer mathematical questions related to the article. The clips this month, from the Colorado State lottery and a Marilyn vos Savant column on probability, involve probability and counting problems.

Informing Practice: Counting Using Sets of Outcomes

2012 ◽  
Vol 18 (3) ◽  
pp. 132-135 ◽  
Author(s):  
Elise Lockwood
Keyword(s):  
Counting Problems

A branch of mathematics—combinatorics—is explored through counting problems.

scholarly journals Automorphisms of models of bounded arithmetic

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