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The Analytic PolynomialTime Hierarchy
 Mathematical Logic Quaterly
, 1997
"... Motivated by results on interactive proof systems we investigate an 98hierarchy over P using word quantifiers as well as two types of set quantifiers. This hierarchy, which extends the (arithmetic) polynomialtime hierarchy, is called the analytic polynomialtime hierarchy. It is shown that every ..."
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Cited by 3 (2 self)
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Motivated by results on interactive proof systems we investigate an 98hierarchy over P using word quantifiers as well as two types of set quantifiers. This hierarchy, which extends the (arithmetic) polynomialtime hierarchy, is called the analytic polynomialtime hierarchy. It is shown
PP IS AS HARD AS THE POLYNOMIALTIME HIERARCHY*
"... Abstract. In this paper, two interesting complexity classes, PP and P, are compared with PH, the polynomialtime hierarchy. It is shown that every set in PH is polynomialtime Turing reducible to a set in PP, and PH is included in BP. 0)P. As a consequence of the results, it follows thatPPPH (or 03P ..."
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Abstract. In this paper, two interesting complexity classes, PP and P, are compared with PH, the polynomialtime hierarchy. It is shown that every set in PH is polynomialtime Turing reducible to a set in PP, and PH is included in BP. 0)P. As a consequence of the results, it follows thatPPPH (or 03
PolynomialTime Hierarchy on Randomized Machines
"... 1 Introduction Proving lower bounds remains one of the most challenging tasks in computationalcomplexity. Satisfiability, the seminal NPcomplete problem, is particularly unyielding in this respect. While we believe that any algorithm for satisfiabilitytakes time linear exponential in the number of ..."
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of variables in the formula, we have been unable to prove superlinear time lower bounds on random access machinesdespite several decades of effort. Additionally, problems complete for higher levels of the polynomialtime hierarchy, while not receiving as much attention, havealso resisted nontrivial time lower
Relating the Bounded Arithmetic and Polynomial Time Hierarchies
 ANNALS OF PURE AND APPLIED LOGIC
, 1994
"... The bounded arithmetic theory S 2 is finitely axiomatized if and only if the polynomial hierarchy provably collapses. If T 2 equals S then T 2 is equal to S 2 and proves that the polynomial time hierarchy collapses to # , and, in fact, to the Boolean hierarchy over # and to # i+1 / ..."
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Cited by 28 (1 self)
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The bounded arithmetic theory S 2 is finitely axiomatized if and only if the polynomial hierarchy provably collapses. If T 2 equals S then T 2 is equal to S 2 and proves that the polynomial time hierarchy collapses to # , and, in fact, to the Boolean hierarchy over # and to # i+1
Bounding Queries in the Analytic PolynomialTime Hierarchy
 Theoretical Computer Science
, 1997
"... In a previous paper the present authors [4] investigated an 98hierarchy over P using word quantifiers as well as two types of set quantifiers, the so called analytic polynomialtime hierarchy. The fact that some constructions there result in a bounded number of oracle queries and the recent PCP re ..."
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In a previous paper the present authors [4] investigated an 98hierarchy over P using word quantifiers as well as two types of set quantifiers, the so called analytic polynomialtime hierarchy. The fact that some constructions there result in a bounded number of oracle queries and the recent PCP
Bounding Queries in the Analytic PolynomialTime Hierarchy
 Theoretical Computer Science
, 1997
"... In a previous paper the present authors [4] investigated an 98hierarchy over P using word quantifiers as well as two types of set quantifiers, the so called analytic polynomialtime hierarchy. The fact that some constructions there result in a bounded number of oracle queries and the recent PCP re ..."
Abstract

Cited by 8 (0 self)
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In a previous paper the present authors [4] investigated an 98hierarchy over P using word quantifiers as well as two types of set quantifiers, the so called analytic polynomialtime hierarchy. The fact that some constructions there result in a bounded number of oracle queries and the recent PCP
Intuitionistic Deductive Databases And The Polynomial Time Hierarchy
, 1997
"... this paper, we establish more comprehensive results by exploring the interaction of negationasfailure with a natural syntactic restriction called linearity. The main result is a tight connection between intuitionistic logic, database queries, and the polynomial time hierarchy. A tight connection w ..."
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Cited by 5 (2 self)
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this paper, we establish more comprehensive results by exploring the interaction of negationasfailure with a natural syntactic restriction called linearity. The main result is a tight connection between intuitionistic logic, database queries, and the polynomial time hierarchy. A tight connection
On the hardness of satisfiability with bounded occurrences in the polynomialtime hierarchy
 THEORY OF COMPUTING
, 2007
"... In 1991, Papadimitriou and Yannakakis gave a reduction implying the NPhardness of approximating the problem 3SAT with bounded occurrences. Their reduction is based on expander graphs. We present an analogue of this result for the second level of the polynomialtime hierarchy based on superconcen ..."
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Cited by 2 (1 self)
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In 1991, Papadimitriou and Yannakakis gave a reduction implying the NPhardness of approximating the problem 3SAT with bounded occurrences. Their reduction is based on expander graphs. We present an analogue of this result for the second level of the polynomialtime hierarchy based
Completeness in the polynomialtime hierarchy: A compendium
 SIGACT News
"... We present a Garey/Johnsonstyle list of problems known to be complete for the second and higher levels of the polynomialtime Hierarchy (polynomial hierarchy, or PH for short). We also include the bestknown hardness of approximation results. The list will be updated as necessary. Updates The compe ..."
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Cited by 27 (2 self)
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We present a Garey/Johnsonstyle list of problems known to be complete for the second and higher levels of the polynomialtime Hierarchy (polynomial hierarchy, or PH for short). We also include the bestknown hardness of approximation results. The list will be updated as necessary. Updates
How Reductions to Sparse Sets Collapse the Polynomialtime Hierarchy: A Primer
, 1993
"... this paper to give simple proofs, in a uniform format, of the major known (pre1992) results relating how polynomialtime reductions of SAT to sparse sets collapse the polynomialtime hierarchy. To help the reader familiar with basic facts of complexity theory follow the main flow of ideas, while ke ..."
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Cited by 13 (0 self)
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this paper to give simple proofs, in a uniform format, of the major known (pre1992) results relating how polynomialtime reductions of SAT to sparse sets collapse the polynomialtime hierarchy. To help the reader familiar with basic facts of complexity theory follow the main flow of ideas, while
Results 1  10
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