Related papers: Polynomial Time and Dependent Types
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…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview…
In this work we present a coupled-cluster theory for the propagation of multireference electronic systems initiating at general quantum mechanical states. Our formalism is based on the infinitesimal analysis of modified cluster operators,…
We give two natural definitions of polynomial-time computability for L2 functions; and we show them incomparable (unless complexity class FP_1 includes #P_1).
This paper introduces and analyzes an improved Q-learning algorithm for discrete-time linear time-invariant systems. The proposed method does not require any knowledge of the system dynamics, and it enjoys significant efficiency advantages…
We present two algorithms for the computation of the Kalman form of a linear control system. The first one is based on the technique developed by Keller-Gehrig for the computation of the characteristic polynomial. The cost is a logarithmic…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
We provide efficient replicable algorithms for the problem of learning large-margin halfspaces. Our results improve upon the algorithms provided by Impagliazzo, Lei, Pitassi, and Sorrell [STOC, 2022]. We design the first…
We consider the problem of data-driven predictive control for an unknown discrete-time linear time-periodic (LTP) system of known period. Our proposed strategy generalizes both Data-enabled Predictive Control (DeePC) and Subspace Predictive…
We present a fundamental improvement of a high polynomial degree time domain cell method recently introduced by the last three authors. The published work introduced a method featuring block-diagonal system matrices where the block size and…
We show that restricting the elimination principle of the natural numbers type in Martin-L\"of Type Theory (MLTT) to a universe of types not containing $\Pi$-types ensures that all definable functions are primitive recursive. This extends…
This paper proposes a reinforcement learning method for controller synthesis of autonomous systems in unknown and partially-observable environments with subjective time-dependent safety constraints. Mathematically, we model the system…
We show that recent approaches of static analysis based on quantitative typing systems can be extended to programming languages with global state. More precisely, we define a call-by-value language equipped with operations to access a…
We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…
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…
Left-right and conjugation actions on matrix tuples have received considerable attention in theoretical computer science due to their connections with polynomial identity testing, group isomorphism, and tensor isomorphism. In this paper, we…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
The outcomes of this paper are twofold. Implicit complexity. We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class PTIME of languages computable in…
We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: (*) Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In…