Syntactic Complexity of Circular Semi-Flower Automata

We investigate the syntactic complexity of certain types of finitely generated submonoids of a free monoid. In fact, we consider those submonoids which are accepted by circular semi-flower automata (CSFA). Here, we show that the syntactic complexity of CSFA with at most one `branch point going in' (bpi) is linear. Further, we prove that the syntactic complexity of $n$-state CSFA with two bpis over a binary alphabet is $2n(n+1)$

An introduction to finite automata and their connection to logic

This is a tutorial on finite automata. We present the standard material on determinization and minimization, as well as an account of the equivalence of finite automata and monadic second-order logic. We conclude with an introduction to the syntactic monoid, and as an application give a proof of the equivalence of first-order definability and aperiodicity

Simultaneous Finite Automata: An Efficient Data-Parallel Model for Regular Expression Matching

Automata play important roles in wide area of computing and the growth of multicores calls for their efficient parallel implementation. Though it is known in theory that we can perform the computation of a finite automaton in parallel by simulating transitions, its implementation has a large overhead due to the simulation. In this paper we propose a new automaton called simultaneous finite automaton (SFA) for efficient parallel computation of an automaton. The key idea is to extend an automaton so that it involves the simulation of transitions. Since an SFA itself has a good property of parallelism, we can develop easily a parallel implementation without overheads. We have implemented a regular expression matcher based on SFA, and it has achieved over 10-times speedups on an environment with dual hexa-core CPUs in a typical case.Comment: This paper has been accepted at the following conference: 2013 International Conference on Parallel Processing (ICPP- 2013), October 1-4, 2013 Ecole Normale Suprieure de Lyon, Lyon, Franc

Logics with rigidly guarded data tests

The notion of orbit finite data monoid was recently introduced by Bojanczyk as an algebraic object for defining recognizable languages of data words. Following Buchi's approach, we introduce a variant of monadic second-order logic with data equality tests that captures precisely the data languages recognizable by orbit finite data monoids. We also establish, following this time the approach of Schutzenberger, McNaughton and Papert, that the first-order fragment of this logic defines exactly the data languages recognizable by aperiodic orbit finite data monoids. Finally, we consider another variant of the logic that can be interpreted over generic structures with data. The data languages defined in this variant are also recognized by unambiguous finite memory automata

Syntactic Complexity of Prefix-, Suffix-, Bifix-, and Factor-Free Regular Languages

The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity $n$ of these languages. We study the syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages. We prove that $n^{n-2}$ is a tight upper bound for prefix-free regular languages. We present properties of the syntactic semigroups of suffix-, bifix-, and factor-free regular languages, conjecture tight upper bounds on their size to be $(n-1)^{n-2}+(n-2)$, $(n-1)^{n-3} + (n-2)^{n-3} + (n-3)2^{n-3}$, and $(n-1)^{n-3} + (n-3)2^{n-3} + 1$, respectively, and exhibit languages with these syntactic complexities.Comment: 28 pages, 6 figures, 3 tables. An earlier version of this paper was presented in: M. Holzer, M. Kutrib, G. Pighizzini, eds., 13th Int. Workshop on Descriptional Complexity of Formal Systems, DCFS 2011, Vol. 6808 of LNCS, Springer, 2011, pp. 93-106. The current version contains improved bounds for suffix-free languages, new results about factor-free languages, and new results about reversa