The literature on programming languages contains an abundance of informal claims on the relative expressive power of programming languages, but there is no framework for formalizing such statements nor for deriving interesting consequences. As a rst step in this direction, we develop a formal notion of expressiveness and investigate its properties. To validate the theory, we analyze some widely...

Abstract We consider quantum chaos diagnostics of the variational circuit states at random parameters and explore their connection to expressibility optimizability. By measuring operator spreading coefficient eigenvalue spectrum modular Hamiltonian reduced density matrix, we identify emergence universal matrix ensembles in high-depth states. The that use spectrum, e.g. entanglement entropy, tur...

In Gödel fuzzy propositional logic, neither conjunction nor implication is expressible (definable) in terms of the remaining three logical connectives. In classical propositional logic, propositions are associated with two truth values 1 (truth) and 0 (falsity). In fuzzy logics further (intermediate) truth values lying between 0 and 1 are possible. Usually the truth values are linearly ordered ...

Cost register automata (CRA) were proposed by Alur et all as an alternative model for weighted automata. In hope of finding decidable subclasses of CRA, they proposed to restrict their model with the copyless restriction but nothing is really know about the structure or properties of this new computational model called copyless CRA. In this paper we study the properties and expressiveness of co...

We present a formal syntax of approximate formulas suited for the logic with counting quantifiers SOLP. This logic was studied by us in [1] where, among other properties, we showed: (i) In the presence of a built–in (linear) order, SOLP can describeNP–complete problems and fragments of it capture classes likeP andNL; (ii) weakening the ordering relation to an almost order we can separate meanin...

Constraint satisfaction problems (CSPs) provide a unified framework for studying a wide variety of computational problems naturally arising in combinatorics, artificial intelligence and database theory. To any finite domain D and any constraint language Γ (a finite set of relations over D), we associate the constraint satisfaction problem CSP(Γ): an instance of CSP(Γ) consists of a list of vari...

The SPIN extension presented in this article is meant as a way to facilitate the modeling and verification of object-oriented programs. It provides means for the formal representation of some run-time mechanisms intensively used in OO software, such as dynamic object creation and deletion, virtual function calls, etc. This article presents a number of language extensions along with their implem...

We review the expressibility of some basic graph properties in certain fragments of Monadic Second-Order logic, like the set of Monadic-NP formulas. We focus on cases where a property and its negation are both expressible in the same (or in closely related) fragments. We examine cases where edge quantifications can be eliminated and cases where they cannot. We compare two logical expressions of...

In this paper, we prove lower bounds on the logical expressibility of optimization problems. There is a significant difference between the expressibilities of decision problems and optimization problems. This is similar to the difference in computation times for the two classes of problems; for example, a 2SAT Horn formula can be satisfied in polynomial time, whereas the optimization version in...