Collapsing Polynomial-Time Degrees
نویسندگان
چکیده
For reducibilities r and r′ such that r is weaker than r′, we say that the r-degree of A, i.e., the class of sets which are r-equivalent to A, collapses to the r′-degree of A if both degrees coincide. We investigate for the polynomial-time bounded many-one, bounded truth-table, truth-table, and Turing reducibilities whether and under which conditions such collapses can occur. While we show that such collapses do not occur for sets which are hard for exponential time, we have been able to construct a recursive set such that its bounded truth-table degree collapses to its many-one degree. The question whether there is a set such that its Turing degree collapses to its many-one degree is still open; however, we show that such a set – if it exists – must be recursive.
منابع مشابه
کاربرد ماشین بردار پشتیبان در طبقهبندی کاربری اراضی حوزه چشمه کیله- چالکرود
Classification of land use extraction always been one of the most important applications of remote sensing and why different methods are created. Over time and with greater accuracy were developed more advanced methods that increase the accuracy and the extraction classes that were closer together in terms of quality are better. SVM is one of these methods in the study of this method for the ex...
متن کاملBinary 3-compressible automata
A finite deterministic automaton A = (Q,Σ, δ) is k-compressible if there is a word w ∈ Σ such that the image of the state set Q under the natural action of w is reduced by at least k states. In such case w is called a k-compressing word for A. It is known that, for any alphabet Σ and any k ≥ 2, there exist words that are k-compressing for each k-compressible automaton with the input alphabet Σ....
متن کاملtitle : Relativized Collapsing Results under Stringent Oracle Access
For relativized arguments, we propose to restrict oracle queries to “stringent” ones. For example, when comparing the power of two machine models relative to some oracle set X, we restrict that machines of both types ask queries from the same segment of the set X. In particular, for investigating polynomial-time (or polynomial-size) computability, we propose polynomial stringency, bounding quer...
متن کاملPolynomial kernels collapse the W-hierarchy
We prove that, for many parameterized problems in the class FPT, the existence of polynomial kernels implies the collapse of the Whierarchy (i.e., W[P] = FPT). The collapsing results are also extended to assumed exponential kernels for problems in the class FPT. In particular, we establish a close relationship between polynomial (and exponential) kernelizability and the existence of sub-exponen...
متن کاملCollapsing Exact Arithmetic Hierarchies
We provide a uniform framework for proving the collapse of the hierarchy NC(C) for an exact arithmetic class C of polynomial degree. These hierarchies collapse all the way down to the third level of the AC-hierarchy, AC3(C). Our main collapsing exhibits are the classes C ∈ {C=NC,C=L,C=SAC,C=P}. NC(C=L) and NC(C=P) are already known to collapse [1,18,19]. We reiterate that our contribution is a ...
متن کامل