Related papers: Algebras for Deterministic Computation Are Inheren…
Students find their first course in Formal Languages and Automata Theory challenging. In addition to the development of formal arguments, most students struggle to understand nondeterministic computation models. In part, the struggle stems…
We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected with partially ordered groups not necessarily with strong unit. In such a case, starting even with an Abelian po-group, we can obtain a…
We define the completion of an associative algebra $A$ in a set $M=\{M_1,\dots,M_r\}$ of $r$ right $A$-modules in such a way that if $\mathfrak a\subseteq A$ is an ideal in a commutative ring $A$ the completion $A$ in the (right) module…
We show that any regular pseudocomplemented Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra determined by a tolerance induced by an irredundant covering.
Modern software is constantly changing. Researchers and practitioners are increasingly aware that verification tools can be impactful if they embrace change through analyses that are compositional and span program versions. Reasoning about…
The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole system-algebra. If the physical algebra commutes with the interaction…
We show that any countably generated von Neumann algebra with specified normal faithful state can arise as the tail algebra of a quantum exchangeable sequence of noncommutative random variables. We also characterize the cases when the state…
A Cylindrical Algebraic Decomposition (CAD) is a decomposition of R^n into a finite collection of semialgebraic cells. A CAD satisfies the "frontier condition" if, for every cell C, there is a collection of cells of the decomposition whose…
General program equivalence is undecidable. However, if we abstract away the semantics of statements, then this problem becomes not just decidable, but practically feasible. For instance, a program of the form "if $b$ then $e$ else $f$"…
Motivated by a need for a model of reversible computation appropriate for a Brownian molecular architecture, the $\aleph$ calculus is introduced. This novel model is declarative, concurrent, and term-based--encapsulating all information…
We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
We propose regular expressions to abstractly model and study properties of resource-aware computations. Inspired by nominal techniques -- as those popular in process calculi -- we extend classical regular expressions with names (to model…
The four-component cat state represents a particularly useful quantum state for realizing fault-tolerant continuous variable quantum computing. While such encoding has been experimentally generated and employed in the microwave regime, the…
Relation algebra and its reducts provide us with a strong tool for reasoning about nondeterministic programs and their partial correctness. Demonic calculus, introduced to model the behaviour of a machine where the demon is in control of…
Distributive laws are important for algebraic reasoning in arithmetic and logic. They are equally important for algebraic reasoning about concurrent programs. In existing theories such as Concurrent Kleene Algebra, only partial correctness…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
We prove that the equational theory of Kleene algebra with commutativity conditions on primitives (or atomic terms) is undecidable, thereby settling a longstanding open question in the theory of Kleene algebra. While this question has also…
The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…
Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main…