Related papers: Algorithmic analysis of systems with affine input …
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
The complexity of computing equilibrium refinements has been at the forefront of algorithmic game theory research, but it has remained open in the seminal class of potential games; we close this fundamental gap in this paper. We first show…
We introduce a novel architecture and computational framework for formal, automated analysis of systems with a broad set of nonlinearities in the feedback loop, such as neural networks, vision controllers, switched systems, and even simple…
In this paper we obtain complexity bounds for computational problems on algebraic power series over several commuting variables. The power series are specified by systems of polynomial equations: a formalism closely related to weighted…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…
Using ideas from automata theory we design a new efficient (deterministic) identity test for the \emph{noncommutative} polynomial identity testing problem (first introduced and studied in \cite{RS05,BW05}). We also apply this idea to the…
We derive novel criteria for designing stabilizing dynamic output-feedback controllers for a class of aperiodic impulsive systems subject to a range dwell-time condition. Our synthesis conditions are formulated as clock-dependent linear…
Computation biology helps to understand all processes in organisms from interaction of molecules to complex functions of whole organs. Therefore, there is a need for mathematical methods and models that deliver logical explanations in a…
We consider a family of quantum spin systems which includes as special cases the ferromagnetic XY model and ferromagnetic Ising model on any graph, with or without a transverse magnetic field. We prove that the partition function of any…
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
The Qth-power algorithm for computing structured global presentations of integral closures of affine domains over finite fields is modified to compute structured presentations of integral closures of ideals in affine domains over finite…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
We provide the first fully polynomial-time randomized approximation scheme for the following two counting problems: 1. Given a Context Free Grammar $G$ over alphabet $\Sigma$, count the number of words of length exactly $n$ generated by…
We study constraint satisfaction problems (CSPs) where the constraint languages are defined by finite automata, giving rise to automata-based CSPs. The key notion is the concept of Automatic Constraint Satisfaction Problem ($AutCSP$), where…
The goal of the paper is two-fold. The first of which is to derive an explicit formula to compute the generating series of a closed-loop system when a plant, given in a Chen-Fliess series description is in multiplicative output feedback…
This paper proposes a novel sliding mode control (SMC) method for a class of affine dynamic systems. In this type of systems, the high-frequency gain matrix (HFGM), which is the matrix multiplying the control vector in the dynamic equation…
For systems described by finite matrices, an affine form is developed for the maps that describe evolution of density matrices for a quantum system that interacts with another. This is established directly from the Heisenberg picture. It…
The goal of this paper is to introduce a new constructive geometric proof of the affine version of Chevalley's Theorem. This proof is algorithmic and a verbatim implementation resulted in an efficient code for computing the constructible…
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…