To provide high performance at practical power levels, tomorrow’s chips will have to consist primarily of application-specic logic that is only powered on when needed. is paper discusses synthesizing such logic from the functional language Haskell. e proposed approach, which consists of rewriting steps that ultimately dismantle the source program into a simple dialect that enables a syntax-dir...

We present the foundations of a verifier for higher-order functional programs with generics and recursive algebraic data types. Our verifier supports finding sound proofs and counterexamples even in the presence of certain quantified invariants and recursive functions. Our approach uses the same language to describe programs and invariants and uses semantic criteria for establishing termination...

A new suboptimal control design technique is proposed for a class of cascaded non-linear systems. The design is based on a forward recursive design rather than a backstepping design, and it utilizes a non-linear tracker derived using the state-dependent algebraic Riccati equation approach. The proposed design has two distinct features. First, it provides suboptimal performance with respect to a...

This paper describes general theory underpinning the operational semantics and the denota-tional Petri net semantics of the box algebra including recursion. For the operational semantics, inductive rules for process expressions are given. For the net semantics, a general mechanism of re-nement and relabelling is introduced, using which the connectives of the algebra are deened. The paper also d...

We introduce a state reenement operator into BPA with recursive speciications and present a comprehensive technical development of the resulting theory, BPA + SR. Our main technical results are that bisimulation is a congruence in BPA+SR and that guarded recursive speciications have unique solutions. We also have that bisimulation remains a congruence if the merge operator of ACP is added to BP...

We have developed an algebraic framework for the study of recursion. For immediate linear recursion, a Horn clause is represented by a relational algebra operator. We show that the set of all such operators forms a closed semiring. In this formalism, query answering corresponds to solving a linear equation. For the first time, we are able to have the query answer expressed in an explicit algebr...

Moore introduced a class of real-valued “recursive” functions by analogy with Kleene’s formulation of the standard recursive functions. While his concise definition inspired a new line of research on analog computation, it contains some technical inaccuracies. Focusing on his “primitive recursive” functions, we pin down what is problematic and discuss possible attempts to remove the ambiguity r...

Recently, using a limit schema, we presented an analog and machine independent algebraic characterization of elementary functions over the real numbers in the sense of recursive analysis. In a different and orthogonal work, we proposed a minimalization schema that allows to provide a class of real recursive functions that corresponds to extensions of computable functions over the integers. Mixi...

We introduce a typed functional programming language LPL(acronym for Light linear Programming Language) in which all valid programs run in polynomial time, and which is complete for polynomial time functions. LPL is based on lambda-calculus, with constructors for algebraic data-types, pattern matching and recursive definitions, and thus allows for a natural programming style. The validity of LP...