Related papers: The Replace Operator
We resolve an open question by determining matching (asymptotic) upper and lower bounds on the state complexity of the operation that sends a language L to (c(L*))*, where c() denotes complement.
Recently, it was shown that any theory of strings containing the string-replace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of…
The explosive rate of information growth and availability often makes it increasingly difficult to locate information pertinent to your needs. These problems are often compounded when keyword based search methodologies are not adequate for…
This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…
Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…
This paper is devoted to conditions defined in terms of the generalized shift operator for a rational number to be representable by certain positive generalizations of $q$-ary expansions.
In this paper, a simple and unified method is developed that predicts the relativistic alterations of physical measures when the behavior of a natural system is characterized by means of a specific operator equation. Separation of variables…
We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…
We introduce a new two-sided type system for verifying the correctness and incorrectness of functional programs with atoms and pattern matching. A key idea in the work is that types should range over sets of normal forms, rather than sets…
In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…
Through duality it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or…
We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
We consider equations arising from rational Lax representations. A general method to construct recursion operators for such equations is given. Several examples are given, including a degenerate bi-Hamiltonian system with a recursion…
In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
By a physical system we recognize a set of propositions about a given system with their truth-values depending on the states of the system. Since every physical system can go from one state in another one, there exists a binary relation on…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…
Sophisticated machine models are increasingly used for high-stakes decisions in everyday life. There is an urgent need to develop effective explanation techniques for such automated decisions. Rule-Based Explanations have been proposed for…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…