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Probabilistic automata constitute a versatile and elegant model for concurrent probabilistic systems. They are equipped with a compositional theory supporting abstraction, enabled by weak probabilistic bisimulation serving as the reference…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
We perform a tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta=\pi$ term. Within the Hamiltonian formulation, this field theory emerges as the finite-temperature partition function of a modified…
This paper is concerned with linear parameter-dependent systems and considers the notion uniform ensemble reachability. The focus of this work is on constructive methods to compute suitable parameter-independent open-loop inputs for such…
This paper presents a probabilistic model validation methodology for nonlinear systems in time-domain. The proposed formulation is simple, intuitive, and accounts both deterministic and stochastic nonlinear systems with parametric and…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
The simulated tempering (ST) is an important method to deal with systems whose phase spaces are hard to sample ergodically. However, it uses accepting probabilities weights which often demand involving and time consuming calculations. Here…
The Curry-Howard correspondence is often called the proofs-as-programs result. I offer a generalization of this result, something which may be called machines as programs. Utilizing this insight, I introduce two new Turing Machines called…
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…
We extended our simulation tool Ntccrt for probabilistic ntcc (pntcc) models. In addition, we developed a verification tool for pntcc models. Using this tool we can prove properties such as the system will go to a successful state with…
In the early 1980s, Selman's seminal work on positive Turing reductions showed that positive Turing reduction to NP yields no greater computational power than NP itself. Thus, positive Turing and Turing reducibility to NP differ sharply…
We introduce a tensor network algorithm for the solution of $p$-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system…
We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can apply to any pair of qubits, starting in a computational basis state. We prove a…
We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is…
The quantum theory involving noncommutative tensionless p-branes is studied following path integral methods. Our procedure allow a simple treatment for generally covariant noncommutative extended systems and it contains, as a particular…
This paper presents a new abstract method for proving lower bounds in computational complexity. Based on the notion of topological and measurable entropy for dynamical systems, it is shown to generalise three previous lower bounds results…
Nondeterministic polynomial-time Blum-Shub-Smale Machines over the reals give rise to a discrete complexity class between NP and PSPACE. Several problems, mostly from real algebraic geometry / polynomial systems, have been shown complete…
In this paper, we study the well-posedness of Poisson-Nernst-Planck system with no-flux boundary condition and singular permanent charges in two dimension. The main difficulty comes from the lack of integrability of singular permanent…
We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In…
We present a new numerical method for solving time dependent Maxwell equations, which is also suitable for general linear hyperbolic equations. It is based on an unstructured partitioning of the spacetime domain into tent-shaped regions…