相关论文: Dyck language and fermionic second quantization: I…

This paper describes an algorithm for the compilation of a two (or more) level orthographic or phonological rule notation into finite state transducers. The notation is an alternative to the standard one deriving from Koskenniemi's work: it…

Recently, we proposed measurement theory ( or. quantum language) as a linguistic turn of quantum mechanics (with the Copenhagen interpretation). This theory has a great power of scientific descriptions. In fact, we have continued asserting…

We propose a new symbolic trace semantics for register automata (extended finite state machines) which records both the sequence of input symbols that occur during a run as well as the constraints on input parameters that are imposed by…

Harnessing the power of dependently typed languages can be difficult. Programmers must manually construct proofs to produce well-typed programs, which is not an easy task. In particular, migrating code to these languages is challenging.…

We analyze fermionic modes as fundamental entities for quantum information processing. To this end we construct a density operator formalism on the underlying Fock space and demonstrate how it can be naturally and unambiguously equipped…

In this paper we discuss two approaches to anomaly-free quantization of a two-dimensional string. The first approach is based on the canonical Dirac prescription of quantization of degenerated systems. At the second approach we "weaken" the…

In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the theory of normal forms for non-commuting operators, and obtain as an application a commutativity criterion for…

We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…

We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…

We consider the problem of determining if a sequence of parentheses is well parenthesized, with a depth of at most h. We denote this language as $Dyck_h$. We study the quantum query complexity of this problem for different h as function of…

Quantum computers have leaped from the theoretical realm into a race to large-scale implementations. This is due to the promise of revolutionary speedups, where achieving such speedup requires designing an algorithm that harnesses the…

We use results on Dyck words and lattice paths to derive a formula for the exact number of binary words of a given length with a given minimal abelian border length, tightening a bound on that number from Christodoulakis et al. (Discrete…

Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…

For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…

Factorization of quantum mechanical Hamiltonians has been a useful technique for some time. This procedure has been given an elegant description by supersymmetric quantum mechanics, and the subject has become well-developed. We demonstrate…

Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…

In this paper we consider introducing careful regularization in the quantization of Maxwell theory in the asymptotic null infinity. This allows systematic discussions of the commutators in various boundary conditions, and application of…

The Dirac theory implies the existence of an internal vector space, in addition to spin space. Using Dirac's coupling of variables in internal space to those in physical space, we construct a new configuration structure for particles in the…

We present a path-integral bosonization approach for systems out of equilibrium based on a duality transformation of the original Dirac fermion theory combined with the Schwinger-Keldysh time closed contour technique, to handle the…

This paper begins with a comprehensive overview of combinatorics on words and symbolic dynamics, covering their historical origins, fundamental concepts, and interconnections. Building upon this foundation, we introduce novel mathematical…