Input-driven multi-counter automata

Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper, we investigate stronger variants of inclusion, equivalence and sequential uniformisation, based on a general notion of transducer resynchronisation, and show their decidability. We also investigate the classes of finite-valued rational transductions and deterministic rational transductions, which are known to have a decidable equivalence problem. We show that sequential uniformisation is also decidable for them.

We introduce the concept of one-time nondeterminism as a new kind of limited nondeterminism for finite state machines and pushdown automata. Roughly speaking, one-time nondeterminism means that at the outset the computation is nondeterministic, but whenever it performs a guess, this guess is fixed for the rest of the computation. We characterize the computational power of one-time nondeterministic finite automata (OTNFAs) and one-time nondeterministic pushdown devices. Moreover, we study the descriptional complexity of these machines. For instance, we show that for an [Formula: see text]-state OTNFA with a sole nondeterministic state, that is nondeterministic for only one input symbol, [Formula: see text] states are sufficient and necessary in the worst case for an equivalent deterministic finite automaton. In case of pushdown automata, the conversion of a nondeterministic to a one-time nondeterministic as well as the conversion of a one-time nondeterministic to a deterministic one turn out to be non-recursive, that is, the trade-offs in size cannot be bounded by any recursive function.

Closure properties and decision problems of dag automata

Iterated sequential transducers as language generating devices

A regular language [Formula: see text] is non-returning if in the minimal deterministic finite automaton accepting it there are no transitions into the initial state. Eom, Han and Jirásková derived upper bounds on the state complexity of boolean operations and Kleene star, and proved that these bounds are tight using two different binary witnesses. They derived tight upper bounds for concatenation and reversal using three different ternary witnesses. These five witnesses use a total of six different transformations. We show that for each [Formula: see text], there exists a ternary witness of state complexity [Formula: see text] that meets the bound for reversal, and restrictions of this witness to binary alphabets meet the bounds for star, product, and boolean operations. Hence all of these operations can be handled simultaneously with a single witness, using only three different transformations. We also derive tight upper bounds on the state complexity of binary operations that take arguments with different alphabets. We prove that the maximal syntactic semigroup of a non-returning language has [Formula: see text] elements and requires at least [Formula: see text] generators. We find the maximal state complexities of atoms of non-returning languages. We show that there exists a most complex sequence of non-returning languages that meet the bounds for all of these complexity measures. Furthermore, we prove there is a most complex sequence that meets all the bounds using alphabets of minimal size.

A theory of timed automata

For the universal hypothesis testing problem, where the goal is to decide between the known null hypothesis distribution and some other unknown distribution, Hoeffding proposed a universal test in the nineteen sixties. Hoeffding's universal test statistic can be written in terms of Kullback-Leibler (K-L) divergence between the empirical distribution of the observations and the null hypothesis distribution. In this paper a modification of Hoeffding's test is considered based on a relaxation of the K-L divergence test statistic, referred to as the mismatched divergence. The resulting mismatched test is shown to be a generalized likelihood-ratio test (GLRT) for the case where the alternate distribution lies in a parametric family of the distributions characterized by a finite dimensional parameter, i.e., it is a solution to the corresponding composite hypothesis testing problem. For certain choices of the alternate distribution, it is shown that both the Hoeffding test and the mismatched test have the same asymptotic performance in terms of error exponents. A consequence of this result is that the GLRT is optimal in differentiating a particular distribution from others in an exponential family. It is also shown that the mismatched test has a significant advantage over the Hoeffding test in terms of finite sample size performance. This advantage is due to the difference in the asymptotic variances of the two test statistics under the null hypothesis. In particular, the variance of the K-L divergence grows linearly with the alphabet size, making the test impractical for applications involving large alphabet distributions. The variance of the mismatched divergence on the other hand grows linearly with the dimension of the parameter space, and can hence be controlled through a prudent choice of the function class defining the mismatched divergence.

Petri Net Languages and Infinite Subsets of [formula omitted

Visibly pushdown languages are an interesting subclass of deterministic context-free languages that can model nonregular properties of interest in program analysis. Such class properly contains typical classes of parenthesized languages such as "parenthesis", "bracketed", "balanced" and "input-driven" languages. It is closed under boolean operations and has decidable decision problems such as emptiness, inclusion and universality. We study the membership problem for visibly pushdown languages, and show that it can be solved in time linear in both the size of the input grammar and the length of the input word. The algorithm relies on a reduction to the reachability problem for game graphs. We also discuss the time complexity of the membership problem for the class of balanced languages which is the largest among those cited above. Besides the intrinsic theoretical interest, we further motivate our main result showing an application to the validation of XML documents against Schema and Document Type Definitions (DTDs).

We introduce and study the model of input-driven queue automata. On such devices, the input letters uniquely determine the operations on the memory store which is organized as a queue. In particular, we consider the case where only a finite number of turns on the queue is allowed. The resulting language families share with regular languages many desirable properties. We show that emptiness and several other problems are decidable. Furthermore, we investigate closure under Boolean operations. The existence of an infinite and tight hierarchy depending on the number of turns is also proved.

Integral sequential word functions and growth equivalence of lindenmayer systems

We investigate finite automata whose state graphs are undirected. This means that for any transition from state p to q consuming some letter a from the input there exists a symmetric transition from state q to p consuming a letter a as well. So, the corresponding language families are subregular and, in particular in the deterministic case, subreversible. In detail, we study the operational descriptional complexity of deterministic and nondeterministic undirected finite automata. To this end, the different types of automata on alphabets with few letters are characterized. Then the operational state complexity of the Boolean operations as well as the operations concatenation and iteration is investigated, where tight upper and lower bounds are derived for unary as well as arbitrary alphabets under the condition that the corresponding language classes are closed under the operation considered.

There are many decision problems in automata theory (including membership, emptiness, emptiness of intersection, inclusion and universality problems) that for some classes of tree automata are NP-hard. The study of their parameterized complexity allows us to find new bounds of their non-polynomial time algorithmic behaviors. We present results of such a study for classical tree automata (TA), rigid tree automata (RTA), tree automata with global equality and disequality (TAGED) and t-DAG automata.KeywordsModel CheckParameterized ComplexityLinear Temporal LogicFinite AutomatonGlobal ConstraintThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Perfect languages, characterized by closure under Boolean operations and decidable emptiness problem, form the basis for decidable automata-theoretic model-checking for the corresponding class of models. Regular languages and visibly pushdown languages are paradigmatic examples of perfect languages. In a previous work authors have established a timed context-sensitive perfect language characterized by multistack pushdown automata (MPA) with an explicit bound on number of rounds where in each round at most one stack is used. This paper complements the results of on bounded-round timed MPA by characterizing an alternative restriction on timed context-sensitive perfect languages called the scope-bounded multi-stack timed push-down automata where every stack symbol must be popped within a bounded number of stack contexts. The proposed model uses visibly-pushdown alphabet and event clocks to recover a bounded-scope MPA with decidable emptiness, closure under Boolean operations, and an equivalent logical characterization.

Automated reasoning about systems with infinite domains requires an extension of automata, and in particular, finite automata, to infinite alphabets. One such model is Variable Finite Automata (VFA). VFAs are finite automata whose alphabet is interpreted as variables that range over an infinite domain. On top of their simple and intuitive structure, VFAs have many appealing properties. One such property is a deterministic fragment (DVFA), which is closed under the Boolean operations, and whose containment and emptiness problems are decidable. These properties are rare amongst the many different models for automata over infinite alphabets. In this paper, we continue to explore the advantages of DVFAs, and show that they have a canonical form, which proves them to be a particularly robust model that is easy to reason about and use in practice. Building on these results, we construct an efficient learning algorithm for DVFAs, based on the \(\textsc {L}^*\) algorithm for regular languages.