Register automata with linear arithmetic

We propose a novel automata model over the alphabet of rational numbers, which we call register automata over the rationals (RA-Q). It reads a sequence of rational numbers and outputs another rational number. RA-Q is an extension of the well-known register automata (RA) over infinite alphabets, which are finite automata equipped with a finite number of registers/variables for storing values. Like in the standard RA, the RA-Q model allows both equality and ordering tests between values. It, moreover, allows to perform linear arithmetic between certain variables. The model is quite expressive: in addition to the standard RA, it also generalizes other well-known models such as affine programs and arithmetic circuits. The main feature of RA-Q is that despite the use of linear arithmetic, the so-called invariant problem---a generalization of the standard non-emptiness problem---is decidable. We also investigate other natural decision problems, namely, commutativity, equivalence, and reachability. For deterministic RA-Q, commutativity and equivalence are polynomial-time inter-reducible with the invariant problem

Discovery of novel Ooceraea (Hymenoptera: Formicidae: Dorylinae) species with 8-segmented antennae from China

Here we describe an Ooceraea species with 8-segmented antennae for the first time. A revised key for all the known species of this genus based on the worker caste is provided

On the satisfiability of indexed linear temporal logics

Indexed Linear Temporal Logics (ILTL) are an extension of standard Linear Temporal Logics (LTL) with quantifications over index variables which range over a set of process identifiers. ILTL has been widely used in specifying and verifying properties of parameterised systems, e.g., in parameterised model checking of concurrent processes. However there is still a lack of theoretical investigations on properties of ILTL, compared to the well-studied LTL. In this paper, we start to narrow this gap, focusing on the satisfiability problem, i.e., to decide whether a model exists for a given formula. This problem is in general undecidable. Various fragments of ILTL have been considered in the literature typically in parameterised model checking, e.g., ILTL formulae in prenex normal form, or containing only non-nested quantifiers, or admitting limited temporal operators. We carry out a thorough study on the decidability and complexity of the satisfiability problem for these fragments. Namely, for each fragment, we either show that it is undecidable, or otherwise provide tight complexity bounds

The Complexity of SORE-definability Problems

Single occurrence regular expressions (SORE) are a special kind of deterministic regular expressions, which are extensively used in the schema languages DTD and XSD for XML documents. In this paper, with motivations from the simplification of XML schemas, we consider the SORE-definability problem: Given a regular expression, decide whether it has an equivalent SORE. We investigate extensively the complexity of the SORE-definability problem: We consider both (standard) regular expressions and regular expressions with counting, and distinguish between the alphabets of size at least two and unary alphabets. In all cases, we obtain tight complexity bounds. In addition, we consider another variant of this problem, the bounded SORE-definability problem, which is to decide, given a regular expression E and a number M (encoded in unary or binary), whether there is an SORE, which is equivalent to E on the set of words of length at most M. We show that in several cases, there is an exponential decrease in the complexity when switching from the SORE-definability problem to its bounded variant

Global model checking on pushdown multi-agent systems

Pushdown multi-agent systems, modeled by pushdown game structures (PGSs), are an important paradigm of infinite-state multi-agent systems. Alternating-time temporal logics are well-known specification formalisms for multi-agent systems, where the selective path quantifier is introduced to reason about strategies of agents. In this paper, we investigate model checking algorithms for variants of alternating-time temporal logics over PGSs, initiated by Murano and Perelli at IJCAI'15. We first give a triply exponential-time model checking algorithm for ATL* over PGSs. The algorithm is based on the saturation method, and is the first global model checking algorithm with a matching lower bound. Next, we study the model checking problem for the alternating-time mu-calculus. We propose an exponential-time global model checking algorithm which extends similar algorithms for pushdown systems and modal mu-calculus. The algorithm admits a matching lower bound, which holds even for the alternation-free fragment and ATL