Working in the untyped lambda calculus, we study Morris’s λ-theory H+. Introduced in 1968, this is the original extensional theory of contextual equivalence. On the syntactic side, we show that this λ-theory validates the ω-rule, thus settling a long-standing open problem. On the semantic side, we provide sufficient and necessary conditions for relational graph models to be fully abstract for H...

We present quantitative analysis of various (syntactic and behavioral) properties of random λ-terms. Our main results are that asymptotically all the terms are strongly normalizing and that any fixed closed term almost never appears in a random term. Surprisingly, in combinatory logic (the translation of the λ-calculus into combinators) the result is exactly opposite. We show that almost all te...

We present quantitative analysis of various (syntactic and behavioral) properties of random λ-terms. Our main results are that asymptotically all the terms are strongly normalizing and that any fixed closed term almost never appears in a random term. Surprisingly, in combinatory logic (the translation of the λ-calculus into combinators) the result is exactly opposite. We show that almost all te...

Abstract Implementing quantum algorithms on realistic devices requires translating high-level global operations into sequences of hardware-native logic gates, a process known as compiling. Physical limitations, such constraints in connectivity and gate alphabets, often result unacceptable implementation costs. To enable successful near-term applications, it is crucial to optimize compilation by...

We suggest new strongly polynomial algorithms for solving linear programs min( ∑ xi|S) with constraints S of the monotonic discounted form xi ≥ λxj + β with 0 < λ < 1. The algorithm for the case when the discounting factor λ is equal for all constraints is O(mn2), whereas the algorithm for the case when λ may vary between the constraints is O(mn2 logm), where n is the number of variables and m ...

This paper fits in the research line of implicit computational complexity (ICC), whose goal is to characterize complexity classes without relying on explicit bounds on resources but instead by considering restrictions on programming languages and calculi. One can distinguish in this body of work between some monovalent characterisations, which provide a language for one given complexity class, ...

migration of virtual machine (vm) is a critical challenge in cloud computing. the process to move vms or applications from one physical machine (pm) to another is known as vm migration. in vm migration several issues should be considered. one of the major issues in vm migration problem is selecting an appropriate pm as a destination for a migrating vm. to face this issue, several approaches are...

In reinforcement learning, the TD(λ) algorithm is a fundamental policy evaluation method with an efficient online implementation that is suitable for large-scale problems. One practical drawback of TD(λ) is its sensitivity to the choice of the step-size. It is an empirically well-known fact that a large step-size leads to fast convergence, at the cost of higher variance and risk of instability....

The OQ(λ) algorithm benefits from an extension of eligibility traces introduced as opposition trace. This new technique is a combination of the idea of opposition and eligibility traces to deal with large state space problems in reinforcement learning applications. In our previous works the comparison of the results of OQ(λ) and conventional Watkins’ Q(λ) reflected a remarkable increase in perf...