We compute the cardinality of the syntactic monoid of the language 0∗ rep b (mN) made of base b expansions of the multiples of the integer m. We also give lower bounds for the syntactic complexity of any (ultimately) periodic set of integers written in base b. We apply our results to some well studied problem: decide whether or not a brecognizable sets of integers is ultimately periodic.

Our work addresses the automatic detection of paraphrastic rephrasing in spoken corpus. The proposed approach is syntagmatic. It is based on paraphrastic rephrasing markers and the specificities of the spoken language. Manual annotation performed by two annotators provides fine-grained and multi-dimensional description of the reference data. Automatic method is proposed in order to decide wheth...

We provide a precise representation for, and a calculation of the length of, possible path independent determinateness hierarchies of Field’s construction in [4]. We further show in the hierarchies Fα of Fieldian truth sets, and Herzberger’s Hα revision sequence starting from any recursive hypothesis for F0 (or H0) that essentially each Hα (or Fα) carries within it the history of the whole prio...

Let K be an anti-ideal of a semigroup (S,=, =, ·, θ) with apartness. A construction of the anti-congruence Q(K) and the quasi-antiorder θ, generated by K, are presented. Besides, a construction of the anti-order relation Θ on syntactic semigroup S/Q(K), generated by θ, is given in Bishop’s constructive mathematics.

We show that coinductive predicates expressing behavioural properties of infinite objects can be themselves expressed as final coalgebras in a category of relations. The well-known case of bisimulation will simply be a special case of such final predicates. We will show how some useful pointwise and mixed properties of streams can be modelled in this way.

Finding models of logical formulas is a challenging problem. For first-order formulas, a finite model can be found by exhaustive search. For many structured problem instances, there is much isomorphism in the search space. This paper proposes general-purpose techniques for eliminating isomorphic subspaces, which can be helpful when the formulas have many predicates. The techniques are based on ...

This paper proposes a method for automatically acquiring strongly-related events from a large corpus using predicateargument co-occurring statistics and case frames. The strongly-related events are acquired in the form of strongly-related two predicates with their relevant arguments. First, strongly-related events are acquired from predicate-argument cooccurring statistics. Then, the remaining ...

We define a new invariant for shift equivalence of sofic shifts. This invariant, that we call the syntactic graph of a sofic shift, is the directed acyclic graph of characteristic groups of the non null regular D-classes of the syntactic semigroup of the shift.

A regular language L over an alphabet A is called piecewise testable if it is a finite boolean combination of languages of the form Aa1A a2A ∗ . . . Aa`A ∗, where a1, . . . , a` ∈ A, ` ≥ 0. An effective characterization of piecewise testable languages was given in 1972 by Simon who proved that a language L is piecewise testable if and only if its syntactic monoid is J -trivial. Nowadays there e...