Search results for "Formal languages"
showing 10 items of 322 documents
The complexity of graph languages generated by hyperedge replacement
1990
Although in many ways, hyperedge replacement graph grammars (HRGs) are, among all graph generating mechanisms, what context-free Chomsky grammars are in the realm of string rewriting, their parsing problem is known to be, in general, NP-complete. In this paper, the main difficulty in HRG parsing is analysed and some conditions on either grammar or input graphs are developed under which parsing can be done in polynomial time. For some of the cases, the parsing problem is shown to be log-space reducible to context-free string parsing.
Patterns in words and languages
2004
AbstractA word p, over the alphabet of variables E, is a pattern of a word w over A if there exists a non-erasing morphism h from E∗ to A∗ such that h(p)=w. If we take E=A, given two words u,v∈A∗, we write u⩽v if u is a pattern of v. The restriction of ⩽ to aA∗, where A is the binary alphabet {a,b}, is a partial order relation. We introduce, given a word v, the set P(v) of all words u such that u⩽v. P(v), with the relation ⩽, is a poset and it is called the pattern poset of v. The first part of the paper is devoted to investigate the relationships between the structure of the poset P(v) and the combinatorial properties of the word v. In the last section, for a given language L, we consider …
Logics and operators
2003
Two connectives are of special interest in metalogical investigations — the connective of implication which is important due to its connections to the notion of inference, and the connective of equivalence. The latter connective expresses, in the material sense, the fact that two sentences have the same logical value while in the strict sense it expresses the fact that two sentences are interderivable on the basis of a given logic. The process of identification of equivalent sentences relative to theories of a logic C defines a class of abstract algebras. The members of the class are called Lindenbaum-Tarski algebras of the logic C. One may abstract from the origin of these algebras and exa…
Resetting of a planar superconducting quantum memory
2009
We consider and analyze a scheme for the reset of a M × N planar array of inductively coupled Josephson flux qubits. We prove that it is possible to minimize the resetting time of an arbitrary chosen row of qubits by properly switching on and off the coupling between pairs of qubits belonging to the same column. In addition, the analysis of the time evolution of the array allows us to single out the class of generalized W states which can be successfully reset.
InternallyK-like spaces and internal inverse limits
2014
Abstract We establish equivalences between compacta that admit mappings that limit to the identity, and compacta that are inverse limits of the images under these maps. Our results have relationships to Mardesic and Segalʼs equivalence between polyhedra-like compacta and inverse limits of polyhedra, to the Anderson–Choquet Embedding Theorem, to approximative absolute neighborhood retracts, and to continua that are approximated from within as defined by C.A. Eberhart and J.B. Fugate.
Minimal Absent Words in Rooted and Unrooted Trees
2019
We extend the theory of minimal absent words to (rooted and unrooted) trees, having edges labeled by letters from an alphabet \(\varSigma \) of cardinality \(\sigma \). We show that the set \(\text {MAW}(T)\) of minimal absent words of a rooted (resp. unrooted) tree T with n nodes has cardinality \(O(n\sigma )\) (resp. \(O(n^{2}\sigma )\)), and we show that these bounds are realized. Then, we exhibit algorithms to compute all minimal absent words in a rooted (resp. unrooted) tree in output-sensitive time \(O(n+|\text {MAW}(T)|)\) (resp. \(O(n^{2}+|\text {MAW}(T)|)\) assuming an integer alphabet of size polynomial in n.
On the Size Complexity of Deterministic Frequency Automata
2013
Austinat, Diekert, Hertrampf, and Petersen [2] proved that every language L that is (m,n)-recognizable by a deterministic frequency automaton such that m > n/2 can be recognized by a deterministic finite automaton as well. First, the size of deterministic frequency automata and of deterministic finite automata recognizing the same language is compared. Then approximations of a language are considered, where a language L′ is called an approximation of a language L if L′ differs from L in only a finite number of strings. We prove that if a deterministic frequency automaton has k states and (m,n)-recognizes a language L, where m > n/2, then there is a language L′ approximating L such that L′ c…
Monadic second-order logic over pictures and recognizability by tiling systems
1994
We show that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system if and only if it is definable in existential monadic second-order logic. As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and matches a natural logic. The proof is based on the Ehrenfeucht-FraIsse technique for first-order logic and an implementation of “threshold counting” within tiling systems.
Monadic Second-Order Logic over Rectangular Pictures and Recognizability by Tiling Systems
1996
Abstract It is shown that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system iff it is definable in existential monadic second-order logic. As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and also matches a natural logic. The proof is based on the Ehrenfeucht–Fraisse technique for first-order logic and an implementation of “threshold counting” within tiling systems.
Recent results on syntactic groups of prefix codes
2012
International audience; We give a simplified presentation of groups in transformation monoids. We use this presentation to describe two recent results on syntactic groups of prefix codes. The first one uses Sturmian words to build finite bifix codes with a given permutation group as syntactic group. The second one describes a class of prefix codes such that all their syntactic groups are cyclic.