In Schapire gave an equivalent characterization of Levin s notion of functions that are polynomial on average This characterization gives a very smooth translation from worst case complexity to average case complexity of the notions for time and space complexity We prove tight space and time hierarchy theorems and discuss the structure of deterministic and nondeterministic average case complexi...

We study the computational complexity of the distance function associated with a polynomial-time computable two-dimensional domains, in the context of the Turing machine-based complexity theory of real functions. It is proved that the distance function is not necessarily computable even if a two-dimensional domain is polynomial-time recognizable. On the other hand, if both the domain and its co...

Considering the Blum, Shub, and Smale computational model for real numbers, extended by Poizat to general structures, classical complexity can be considered as the restriction to finite structures of a more general notion of computability and complexity working over arbitrary structures. In a previous paper, we showed that the machine-independent characterization of Bellantoni and Cook of seque...

Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...

We propose a low complexity iterative multiuser decoder. We perform the multiuser a-posteriori probability calculation based on the marginalization of probabilities over a subset of the P highest probable sequences. Given a K user symmetric channel this list may be approximated closely with per-bit computational complexity O K P 2K logK . We further show that for any multiuser system possessing...

An oracle Turing machine M has the following additional features: – an additional tape (= query tape) – three additional states: query state q?, answer states qYES, qNO Suppose that M has an oracle for the problem A. Then the call of the oracle works as follows: If M is in state q?, then M decides if the string z on the query tape is a positive instance of A or not. ⇒ M either enters state qYES...

We describe some results inspired to Lafont’s Soft Linear Logic (SLL) which is a subsystem of second-order linear logic with restricted rules for exponentials, correct and complete for polynomial time computations. SLL is the basis for the design of type assignment systems for lambda-calculus, characterizing the complexity classes PTIME, PSPACE and NPTIME. PTIME is characterized by a type assig...

The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f . This observation has been a source of many lower bounds on quantum algorithms. It has been an open problem whether this lower bound is tight. We exhibit a function with polynomial degree M and quantum query complexity Ω(M). This is the first superlinear separation bet...

We present separation results on genuinely (or strongly) time bounded sequential, parallel and non-deterministic complexity classes deened by RAMs with xed set of arithmetic operations. In particular, we separate non-uniform polynomial time from non-uniform parallel polynomial time for the set of operations f+; ?; g (answering a question of M 88]), and uniform deterministic polynomial time from...

In this paper, we study the relationship between the approximability and the parameterized complexity of NP optimization problems. We introduce a notion of polynomial fixed-parameter tractability and prove that, under a very general constraint, an NP optimization problem has a fully polynomial time approximation scheme if and only if the problem is polynomial fixed-parameter tractable. By enfor...