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Mathematics, Computer Science, Generalization, Rewriting, Tree Adjoining Grammar, and 11 moreSyntactic Pattern Recognition, Isotype Picture Language, Tile, MFCS, Syntactic, Rule-Based Machine Translation, Picture Grammar, Mathematical Foundations of Computer Science, Tiling, phrase structure grammar, and Polynomial Time
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We characterize rings whose multiplicative subsemigroups containing 0 and the additive inverse of each element are subrings. In addition we consider commutative rings for which every non-constant multiplicative endormorphism that... more
We characterize rings whose multiplicative subsemigroups containing 0 and the additive inverse of each element are subrings. In addition we consider commutative rings for which every non-constant multiplicative endormorphism that preserves additive inverses is a ring endomorphism, and we show that they belong to one of three easily-described classes of rings.
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Fuzzy aggregation is the way in which different contributions to the same fuzzy fact are merged together to obtain a possibility distribution representative of the acquired knowledge. The choice of the aggregation function is a... more
Fuzzy aggregation is the way in which different contributions to the same fuzzy fact are merged together to obtain a possibility distribution representative of the acquired knowledge. The choice of the aggregation function is a fundamental step in the definition of inference framework. In most cases aggregation has some monotonicity property and this can lead to saturation problems in complex frameworks, particularly in stateful rational agents. In this paper, we propose an extension to the fuzzy aggregation to handle these cases and apply fuzzy reasoning to complex KBs. We especially focus on Mamdani inference framework, where aggregation is implemented by a triangular conorm.
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A new class of languages, called multi-push-down (mpd), that generalize the classical context-free (cf, or Chomsky type 2) ones is introduced. These languages preserve some important properties of cf languages: a generalization of the... more
A new class of languages, called multi-push-down (mpd), that generalize the classical context-free (cf, or Chomsky type 2) ones is introduced. These languages preserve some important properties of cf languages: a generalization of the Chomsky-Schützenberger homomorphic characterization theorem, the Parikh theorem and a “pumping lemma” are proved. Multi-push-down languages are an AFL. Their recognizers are automata equipped with a multi-push-down tape. Multi-push-down languages form a hierarchy based on the number of push-down tapes.
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A finite deterministic automaton A = (Q,, ) is k-com- pressible if there is a word w 2 + such that the image of the state set Q under the natural action of w is reduced by at least k states. In such case w is called a k-compressing word... more
A finite deterministic automaton A = (Q,, ) is k-com- pressible if there is a word w 2 + such that the image of the state set Q under the natural action of w is reduced by at least k states. In such case w is called a k-compressing word forA. It is known that, for any alphabet and any k 2, there exist words that are k-compressing for each k-compressible automaton with the input alphabet . Such words are called k-collapsing. It has been proved that recognizing 2- collapsing words over a 2-element alphabet may be done in polynomial time, while recognizing 2-collapsing words over an alphabet of size 3 is co-NP-complete. A natural question in this context, whether recog- nizing 3-collapsing words over a 2-element alphabet is easy or hard, has remained open. In this paper we provide results on 3-compressible bi- nary automata, which allow to prove that that the latter problem is co-NP-complete.
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A finite deterministic (semi)automaton A = (Q, Σ, δ) is k-compressible if there is some word w ∈ Σ + such that theimage of its state set Q under the natural action of w is reduced by at least k states. Such word w, if it exists, is... more
A finite deterministic (semi)automaton A = (Q, Σ, δ) is k-compressible if there is some word w ∈ Σ + such that theimage of its state set Q under the natural action of w is reduced by at least k states. Such word w, if it exists, is calleda k-compressing word for A and A is said to be k-compressed by w. A word is k-collapsing if it is k-compressing foreach k-compressible automaton, and it is k-synchronizing if it is k-compressing for all k-compressible automata withk+1 states. We compute a set W of short words such that each 3-compressible automaton on a two-letter alphabetis 3-compressed at least by a word in W. Then we construct a shortest common superstring of the words in W and,with a further refinement, we obtain a 3-collapsing word of length 53. Moreover, as previously announced, we showthat the shortest 3-synchronizing word is not 3-collapsing, illustrating the new bounds 34 ≤ c(2, 3) ≤ 53 for the length c(2, 3) of the shortest 3-collapsing word on a two-letter alphabet.
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Linear congruences on a free monoid X ∗ {X^{\ast }} coincide with the congruences on X ∗ {X^{\ast }} induced by nontrivial homomorphisms into the additive group of integers. For a finite X X , we characterize abstractly several classes of... more
Linear congruences on a free monoid X ∗ {X^{\ast }} coincide with the congruences on X ∗ {X^{\ast }} induced by nontrivial homomorphisms into the additive group of integers. For a finite X X , we characterize abstractly several classes of linear congruences on X ∗ {X^{\ast }} , in particular, π \pi -linear congruences, called p p -linear and determined by Reis, ξ \xi -linear congruences, introduced by Petrich and Thierrin, and general linear congruences, introduced by the authors. These characterizations include descriptions involving maximality as prefix congruences.
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In this paper conditions of M-symmetry, strong, semimodularity and θ-modularity for the congruence lattice L (S) of a regular ω-semigroup S are studied. They are proved to be equivalent to modularity. Moreover it is proved that the kernel... more
In this paper conditions of M-symmetry, strong, semimodularity and θ-modularity for the congruence lattice L (S) of a regular ω-semigroup S are studied. They are proved to be equivalent to modularity. Moreover it is proved that the kernel relation is a congruence on L(S) if and only if L(S) is modular, generalizing an analogous result stated by Petrich for bisimple ω-semigroups.
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Piochi in [10] gives a description of the least commutative congruence γ of an inverse semigroup in terms of congruence pairs and generalizes to inverse semigroups the notion of solvability. The object of this paper is to give an explicit... more
Piochi in [10] gives a description of the least commutative congruence γ of an inverse semigroup in terms of congruence pairs and generalizes to inverse semigroups the notion of solvability. The object of this paper is to give an explicit construction of λ for simple regular ω-semigroups exploiting the work of Baird on congruences on such semigroups. Moreover the connection between the solvability classes of simple regular ω-semigroups and those of their subgroups is studied.
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The Associative Language Description model (ALD) is a combination of locally testable and constituent structure ideas. It is consistent with current views on brain organization and can rather conveniently describe typical technical... more
The Associative Language Description model (ALD) is a combination of locally testable and constituent structure ideas. It is consistent with current views on brain organization and can rather conveniently describe typical technical languages such as Pascal or HTML. ALD languages are strictly enclosed in context-free languages but in practice the ALD model equals CF grammars in explanatory adequacy. Various properties of ALD have been investigated, but many theoretical questions are still open. For instance, it is unknown, at the present, whether the ALD family includes the regular languages. Here it is proved that several known classes of regular languages are ALD: threshold locally testable languages, group languages, positive commutative languages and commutative languages on 2-letter alphabets. Moreover, we show that there is an ALD language in each level of (restricted) star height hierarchy. These results seem to show that ALD languages are well-distributed over the class of re...
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Automata, Logic and Semantics Given a word w over a finite alphabet Sigma and a finite deterministic automaton A = < Q,Sigma,delta >, the inequality vertical bar delta(Q,w)vertical bar <= vertical bar Q vertical bar - k means... more
Automata, Logic and Semantics Given a word w over a finite alphabet Sigma and a finite deterministic automaton A = < Q,Sigma,delta >, the inequality vertical bar delta(Q,w)vertical bar <= vertical bar Q vertical bar - k means that under the natural action of the word w the image of the state set Q is reduced by at least k states. The word w is k-collapsing (k-synchronizing) if this inequality holds for any deterministic finite automaton ( with k + 1 states) that satisfies such an inequality for at least one word. We prove that for each alphabet Sigma there is a 2-collapsing word whose length is vertical bar Sigma vertical bar(3)+6 vertical bar Sigma vertical bar(2)+5 vertical bar Sigma vertical bar/2. Then we produce shorter 2-collapsing and 2-synchronizing words over alphabets of 4 and 5 letters.
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A word w over a finite alphabet Σ is n-collapsing if for an arbitrary DFA A = 〈Q,Σ, δ〉, the inequality ∣δ(Q,w)∣ ≤ ∣Q∣ - n holds provided that ∣δ(Q, u)∣ ≤ ∣Q∣ - n for some word u ∈, Σ+ (depending on A ).We give a new algorithm to test... more
A word w over a finite alphabet Σ is n-collapsing if for an arbitrary DFA A = 〈Q,Σ, δ〉, the inequality ∣δ(Q,w)∣ ≤ ∣Q∣ - n holds provided that ∣δ(Q, u)∣ ≤ ∣Q∣ - n for some word u ∈, Σ+ (depending on A ).We give a new algorithm to test whether a word w is 2-collapsing. In contrast to our previous group-theoretic algorithm, the present algorithm is of a geometric nature, and if the word w ∈, Σ* is not 2-collapsing, it directly produces a DFA A w = 〈Q,Σ, δ〉 such that ∣Q∣ w∣, 4}, ∣δ(Q, u)∣ ≤ ∣Q∣- 2 for some word u ∈, Σ*, but ∣δ(Q,w)∣ ≥ ∣Q∣ - 1.
ABSTRACT It is known that the satisfiability problem for equations over free partially commutative monoids is decidable but computationally hard. In this paper we consider the satisfiability problem for equations over free partially... more
ABSTRACT It is known that the satisfiability problem for equations over free partially commutative monoids is decidable but computationally hard. In this paper we consider the satisfiability problem for equations over free partially commutative monoids under the constraint that the solution is a subset of the alphabet. We prove that this problem is NP-complete for quadratic equations and that its uniform version is NP-complete for linear equations.
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The aim of this paper is to collect definitions and results on t he main classes of 2D languages introduced with the attempt of generalizing regular and context-free string languages and in same time preserving some of their nice... more
The aim of this paper is to collect definitions and results on t he main classes of 2D languages introduced with the attempt of generalizing regular and context-free string languages and in same time preserving some of their nice properties. Almost all the models here described are based on tiles. So we also summarize some results on Wang tiles and