522 research outputs found
Presenting Distributive Laws
Distributive laws of a monad T over a functor F are categorical tools for
specifying algebra-coalgebra interaction. They proved to be important for
solving systems of corecursive equations, for the specification of well-behaved
structural operational semantics and, more recently, also for enhancements of
the bisimulation proof method. If T is a free monad, then such distributive
laws correspond to simple natural transformations. However, when T is not free
it can be rather difficult to prove the defining axioms of a distributive law.
In this paper we describe how to obtain a distributive law for a monad with an
equational presentation from a distributive law for the underlying free monad.
We apply this result to show the equivalence between two different
representations of context-free languages
Understanding the Complex Underlying Causes of the Rise of ISIS in Iraq and Syria
How can we understand the complex underlying causes of the rise of ISIS in Iraq and Syria? Did the United States create a āvacuumā in the Middle East that allowed ISIS to come to power? To what extent if true, is this argument a simplification? This thesis will argue that there were in fact multiple variables that led to the rise of ISIS in Syria and Iraq. From a historical aspect, it will examine the regimes within two the countries, analyzing the complex nature of each. This will explain the oppression that many faced. This thesis will also examine the political chaos that dates back decades. The ethnic divide within Syria and Iraq will also be discussed. Analyzing these complex factors will show how ISIS came to power in the Middle East
Sound and complete axiomatizations of coalgebraic language equivalence
Coalgebras provide a uniform framework to study dynamical systems, including
several types of automata. In this paper, we make use of the coalgebraic view
on systems to investigate, in a uniform way, under which conditions calculi
that are sound and complete with respect to behavioral equivalence can be
extended to a coarser coalgebraic language equivalence, which arises from a
generalised powerset construction that determinises coalgebras. We show that
soundness and completeness are established by proving that expressions modulo
axioms of a calculus form the rational fixpoint of the given type functor. Our
main result is that the rational fixpoint of the functor , where is a
monad describing the branching of the systems (e.g. non-determinism, weights,
probability etc.), has as a quotient the rational fixpoint of the
"determinised" type functor , a lifting of to the category of
-algebras. We apply our framework to the concrete example of weighted
automata, for which we present a new sound and complete calculus for weighted
language equivalence. As a special case, we obtain non-deterministic automata,
where we recover Rabinovich's sound and complete calculus for language
equivalence.Comment: Corrected version of published journal articl
Jay Leno and Abstract Algebra
The Jay Leno skit Jaywalking, showing ordinary people struggling to answer basic questions, is both entertaining and applicable to teaching. This article describes how an instructor can strengthen students\u27 conceptual understanding by creating an element of confusion, or cognitive dissonance, in the students\u27 minds using Jaywalking-style interactions in the classroom
Interacting via the Heap in the Presence of Recursion
Almost all modern imperative programming languages include operations for
dynamically manipulating the heap, for example by allocating and deallocating
objects, and by updating reference fields. In the presence of recursive
procedures and local variables the interactions of a program with the heap can
become rather complex, as an unbounded number of objects can be allocated
either on the call stack using local variables, or, anonymously, on the heap
using reference fields. As such a static analysis is, in general, undecidable.
In this paper we study the verification of recursive programs with unbounded
allocation of objects, in a simple imperative language for heap manipulation.
We present an improved semantics for this language, using an abstraction that
is precise. For any program with a bounded visible heap, meaning that the
number of objects reachable from variables at any point of execution is
bounded, this abstraction is a finitary representation of its behaviour, even
though an unbounded number of objects can appear in the state. As a
consequence, for such programs model checking is decidable.
Finally we introduce a specification language for temporal properties of the
heap, and discuss model checking these properties against heap-manipulating
programs.Comment: In Proceedings ICE 2012, arXiv:1212.345
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