Related papers: Intrinsic Sequentiality in P: Causal Limits of Par…
Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite ($*$-finite) number of bits while keeping the finite…
We show that, for all reasonable functions $T(n)=o(n\log n)$, we can algorithmically verify whether a given one-tape Turing machine runs in time at most $T(n)$. This is a tight bound on the order of growth for the function $T$ because we…
The present work proves that P=NP. The proof, presented in this work, is a constructive one: the program of a polynomial time deterministic multi-tape Turing machine M_ExistsAcceptingPath, that determines if there exists an accepting…
Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…
Classical circuit complexity characterizes parallel computation in purely combinatorial terms, ignoring the physical constraints that govern real hardware. The standard classes $\mathbf{NC}$, $\mathbf{AC}$, and $\mathbf{TC}$ treat unlimited…
We study the possibility of designing $N^{o(1)}$-round protocols for problems of substantially super-linear polynomial-time (sequential) complexity in the model of Massively Parallel Computation, where $N$ is the input size. We show that if…
Random instances of feedforward Boolean circuits are studied both analytically and numerically. Evaluating these circuits is known to be a P-complete problem and thus, in the worst case, believed to be impossible to perform, even given a…
Determining the degree of inherent parallelism in classical sequential algorithms and leveraging it for fast parallel execution is a key topic in parallel computing, and detailed analyses are known for a wide range of classical algorithms.…
In typical embedded applications, the precise execution time of the program does not matter, and it is sufficient to meet a real-time deadline. However, modern applications in information security have become much more time-sensitive, due…
We investigate whether there are inherent limits of parallelization in the (randomized) massively parallel computation (MPC) model by comparing it with the (sequential) RAM model. As our main result, we show the existence of hard functions…
A polynomial Turing kernel for some parameterized problem $P$ is a polynomial-time algorithm that solves $P$ using queries to an oracle of $P$ whose sizes are upper-bounded by some polynomial in the parameter. Here the term "polynomial"…
In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are…
Deterministic execution offers many benefits for debugging, fault tolerance, and security. Running parallel programs deterministically is usually difficult and costly, however - especially if we desire system-enforced determinism, ensuring…
Discovering causal relationships from observational data is a crucial problem and it has applications in many research areas. The PC algorithm is the state-of-the-art constraint based method for causal discovery. However, runtime of the PC…
This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named…
Born in the intersection between quantum mechanics and general relativity, indefinite causal structure is the idea that in the continuum of time, some sets of events do not have an inherent causal order between them. Process matrices,…
In this paper, we study the graph realization problem in the Congested Clique model of distributed computing under crash faults. We consider {\em degree-sequence realization}, in which each node $v$ is associated with a degree value $d(v)$,…
Timing side-channels represent an insidious security challenge for cloud computing, because: (a) massive parallelism in the cloud makes timing channels pervasive and hard to control; (b) timing channels enable one customer to steal…
P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…