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Rensets and Renaming-Based Recursion for Syntax with Bindings Extended Version
We introduce renaming-enriched sets ( rensets for short), which are algebraic structures axiomatizing fundamental properties of renaming (also known...
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Recursion
In nature and mathematics, you can find the topic self-similarity or recurring structures, such as snowflakes, fractals, and Julia sets, which are...
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Recursion
In nature and mathematics, you can find the topic self-similarity or recurring structures, such as snowflakes or fractals and Julia sets, which are...
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Advanced Recursion
In this chapter, you will explore some advanced aspects around recursion. You’ll start with the optimization technique called memoization. After...
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Recursion Advanced
In this chapter, you explore some more advanced aspects around recursion. You start with the optimization technique called memoization. After that,...
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The Second Recursion Theorem
The recursion theorem is attributed to Kleene, but it was embedded in a somewhat different format in Gödel’s first incompleteness theorem proof...
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Tail Recursion Transformation for Invertible Functions
Tail recursive functions allow for a wider range of optimisations than general recursive functions. For this reason, much research has gone into the...
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Deterministic Recursion to Target Class Classification
AbstractFormal mathematical description and analysis of the mathematical model of the problem from the field of medicine about adaptation of dynamic...
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Natural Numbers, Mathematical Induction, Recursion
At the end of this chapter...
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Rensets and Renaming-Based Recursion for Syntax with Bindings
I introduce renaming-enriched sets (rensets for short), which are algebraic structures axiomatizing fundamental properties of renaming (also known as...
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Sequences, Induction and Recursion
We review three related topics in this chapter: sequences, induction and recursion. A sequence is an ordered list of elements and is a function from...
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Teaching Recursion in High School
There is little doubt about both the importance and at the same time difficulty of teaching recursion as part of any sophisticated programming...
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Exceptions, Move Constructors and =, Recursion, and O notation
One needful thing – a better way of handling error conditions – and a few very-nice-to-haves: more efficient copying ("move" functions), functions...
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A Sound Strategy to Compile General Recursion into Finite Depth Pattern Matching
Programming languages are popular and diverse, and the convenience of programmatically changing the behavior of complex systems is attractive even...
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Flattening Karatsuba’s Recursion Tree into a Single Summation
The recursion tree resulting from Karatsuba’s formula is built here using an interleaved splitting scheme rather than the traditional left/right one....
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Recycling Outputs as Inputs: Induction and Recursion
Thisinput chapterrecursion introduces inductioninduction and recursion, which are omnipresent in computer science and logic. The simplest context in...
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Exploring recursive neural networks for compact handwritten text recognition models
This paper addresses the challenge of deploying recognition models in specific scenarios in which memory size is relevant, such as in low-cost...
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A Characterization of Functions over the Integers Computable in Polynomial Time Using Discrete Ordinary Differential Equations
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations....
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Complexity Analysis
This Chapter advocates a structure-oriented approach to simplify and generalize complexity investigations. The DIAGONALIZATION and REDUCTION methods...
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Fantastic Morphisms and Where to Find Them
Structured recursion schemes have been widely used in constructing, optimizing, and reasoning about programs over inductive and coinductive...