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1

Deriving Efficient Sequential and Parallel Generators for Closed Simply-Typed Lambda Terms and Normal Forms

Tarau Paul

Fundamenta Informaticae

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2020

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Vol. 177, nr 3/4

385--415

EN

Contrary to several other families of lambda terms, no closed formula or generating function is known and none of the sophisticated techniques devised in analytic combinatorics can currently help with counting or generating the set of simply-typed closed lambda terms of a given size. Moreover, their asymptotic scarcity among the set of closed lambda terms makes counting them via brute force generation and type inference quickly intractable, with previous published work showing counts for them only up to size 10. By taking advantage of the synergy between logic variables, unification with occurs check and efficient backtracking in today’s Prolog systems, we climb 4 orders of magnitude above previously known counts by deriving progressively faster sequential Prolog programs that generate and/or count the set of closed simply-typed lambda terms of sizes up to 14. Similar counts for closed simply-typed normal forms are also derived up to size 14. Finally, we devise several parallel execution algorithms, based on generating code to be uniformly distributed among the available cores, that push the counts for simply typed terms up to size 15 and simply typed normal forms up to size 16. As a remarkable feature, our parallel algorithms are linearly scalable with the number of available cores.

2

Global Stability Analysis of Logistically Grown SIR Model with Loss of Immunity, Inhibitory Effect, Crowding Effect and its Protection Measure

Ghosh U., Sarkar S.

Computational Methods in Science and Technology

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2018

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Vol. 24, No. 2

125--141

EN

In this paper we have considered an SIR model with logistically grown susceptible in which the rate of incidence is directly affected by the inhibitory factors of both susceptible and infected populations and the protection measure for the infected class. Permanence of the solutions, global stability and bifurcation analysis in the neighborhood of equilibrium points has been investigated here. The Center manifold theory is used to find the direction of bifurcations. Finally numerical simulation is carried out to justify the theoretical findings.

3

Gauss–Manin connections for boundary singularities and isochore deformations

Kourliouros K.

Demonstratio Mathematica

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2015

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Vol. 48, nr 2

250--288

EN

We study here the relative cohomology and the Gauss–Manin connections associated to an isolated singularity of a function on a manifold with boundary, i.e. with a fixed hyperplane section. We prove several relative analogs of classical theorems obtained mainly by E. Brieskorn and B. Malgrange, concerning the properties of the Gauss–Manin connection as well as its relations with the Picard–Lefschetz monodromy and the asymptotics of integrals of holomorphic forms along the vanishing cycles. Finally, we give an application in isochore deformation theory, i.e. the deformation theory of boundary singularities with respect to a volume form. In particular, we prove the relative analog of J. Vey’s isochore Morse lemma, J.-P. Françoise’s generalisation on the local normal forms of volume forms with respect to the boundary singularity-preserving diffeomorphisms, as well as M. D. Garay’s theorem on the isochore version of Mather’s versal unfolding theorem.

4

On Normal Forms and Erasing Rules in Path Controlled Grammars

Koutnŷ J., Meduna A.

Schedae Informaticae

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2013

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Vol. 22

9--18

EN

This paper discusses path controlled grammars { context-free gram- mars with a root-to-leaf path in their derivation trees restricted by a control language. First, it investigates the impact of erasing rules on the generative power of path controlled grammars. Then, it establishes two Chomsky-like normal forms for path controlled grammars - the first allows unit rules, the second allows just one erasing rule.

5

Dimension Reduction and Domains of Attraction of Nonlinear Dynamical Systems

Hochlenert D.

Machine Dynamics Research

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2011

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Vol. 35, No. 4

32-48

EN

The appropriate modeling of technical systems usually results in dynamical systems having many or even an infinite number of degrees of freedom. Moreover, nonlinearities play an important role in many applications, so that the arising systems of nonlinear differential equations are difficult to analyze. However, it is well known that the asymptotic behavior of some high dimensional systems can be described by corresponding systems of much smaller dimension. The present paper deals with the dimension reduction of nonlinear systems close to a bifurcation point. Using the ideas of normal form theory, the asymptotic dynamics of the system is extracted by a nonlinear coordinate transformation. The solutions of the reducedordsr system are analyzed analytically with respect to their stability and their domains of attraction. Furthermore, the inverse of the near-identity transformations is used to construct adapted Lyapunov functions for the original system to estimate the attractors of the solutions as well. The procedure is applied to the Duffing equation and the equations of motion of a railway wheelset and compared with numerical solutions.

6

A P Systems Flat Form Preserving Step-by-step Behaviour

Barbuti R., Maggiolo-Schettini A., Milazzo P., Tini S.

Fundamenta Informaticae

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2008

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Vol. 87, nr 1

1-34

EN

Starting from a compositional operational semantics of transition P Systems we have previously defined, we face the problem of developing an axiomatization that is sound and complete with respect to some behavioural equivalence. To achieve this goal, we propose to transform the systems into a normal form with an equivalent semantics. As a first step, we introduce axioms which allow the transformation of membrane structures into flat membranes. We leave as future work the further step that leads to the wanted normal form.

7

A comprehensive setting for matching and unification over iterative terms

Intrigila B., Inverardi P., Zilli M.V.

Fundamenta Informaticae

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1999

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Vol. 39, Nr 3

273-304

EN

Terms finitely representing infinite sequences of finite first-order terms have received attention by several authors. In this paper, we consider the class of recurrent terms proposed by H. Chen and J. Hsiang, and we extend it to allow infinite terms. This extension helps in clarifying the relationships between matching and unification over the class of terms we consider, that we call iterative terms. In fact, it holds that if a term s matches a term t by a substitution G, then the limit of iterations of the matching G, if it exists, is a most general unifier of s and t. A crucial feature of iterative terms is the notion of maximally-folded normal form that allows for a comprehensive treatment of both finite and infinite iterative terms. In this setting, infinite terms can be simply characterized as limits of sequences of finite terms. For finite terms we positively settle an open problem of H. Chen and J. Hsiang on the number of most general unifiers for a pair of terms.