Many familiar models of the untyped lambda calculus are constructed by order theoretic methods. This paper provides some basic new facts about ordered models of the lambda calculus. We show that in any partially ordered model that is complete for the theory of βor βη-conversion, the partial order is trivial on term denotations. Equivalently, the open and closed term algebras of the untyped lamb...

We apply the proper orthogonal decomposition (POD) to the nonlinear Schrödinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic midpoint rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations...

This is a paper on reduction of order of Hamiltonian systems using first integrals, where by order we mean the number of independent variables in the system. In the Hamiltonian case, Noether’s theorem (to be proved below) says that first integrals are equivalent to symmetries of the system and, hence, we could use Sophus Lie’s standard order reduction techniques to accomplish this. The story is...

This paper aims at making partial-order reduction independent of the modeling language. To this end, we present a guard-based method which is a generalpurpose implementation of the stubborn set method. We approach the implementation through so-called necessary enabling sets and do-not-accord sets, and give an algorithm suitable for an abstract model checking interface. We also introduce necessa...

This paper reexamines two results dealing with ample-set-based Partial Order Reduction (POR) for explicit-state model checking. The first is a theorem asserting that POR and “on-the-fly” model checking can be safely combined. It is shown that the proof of this theorem contains a gap, though I am not aware of a counterexample to the theorem itself. The second result asserts that a specific relat...

Model order reduction is a mathematical technique to transform nonlinear dynamical models into smaller ones, that are easier to analyze. In this paper we demonstrate how model order reduction can be applied to nonlinear electronic circuits. First we give an introduction to this important topic. For linear time-invariant systems there exist already some well-known techniques, like Truncated Bala...

We present an algorithm for partial order reduction in the context of a countable universe of deterministic actions, of which finitely many are enabled at any given state. This means that the algorithm is suited for a setting in which resources, such as processes or objects, are dynamically created and destroyed, without an a priori bound. The algorithm relies on abstract enabling and disabling...

This work reports new approaches for order reduction of nonlinear systems with time periodic coefficients. First, the equations of motion are transformed using the Lyapunov-Floquet (LF) transformation, which makes the linear part of new set of equations time invariant. At this point, either linear or nonlinear order reduction methodologies can be applied. The linear order reduction technique is...

Partial order reduction methods combat state explosion by exploring only a part of the full state space. In each state a subset of enabled transitions is selected using well-established criteria. Typically such criteria are based on an upper approximation of dependencies between transitions. An additional heuristic is needed to ensure that currently disabled transitions stay disabled in the dis...

Dynamic Partial Order Reduction (DPOR) is a powerful technique used in verification and testing to reduce the number of equivalent executions explored. Two executions are equivalent if they can be obtained from each other by swapping adjacent, non-conflicting (independent) execution steps. Existing DPOR algorithms rely on a notion of independence that is context-insensitive, i.e., the execution...