Structure preserving transformations on non-left-recursive grammars

We will be concerned with grammar covers, The first part of this paper presents a general framework for covers. The second part introduces a transformation from nonleft-recursive grammars to grammars in Greibach normal form. An investigation of the structure preserving properties of this transformation, which serves also as an illustration of our framework for covers, is presented

The Inclusion Problem for Some Subclasses of Context-Free Languages

By a reduction to Post's Correspondence Problem we provide a direct proof of the known fact that the inclusion problem for unambiguous context-free grammars is undecidable. The argument or some straightforward modification also applies to some other subclasses of context-free languages such as linear languages, sequential languages, and DSC-languages (i.e., languages generated by context-free grammars with disjunct syntactic categories). We also consider instances of the problem "Is L(D_1 )\subseteq L(D_2 )^ ?"where $D_1$ and $D_2$ are taken from possibly different descriptor families of subclasses of context-free languages

Highly Undecidable Problems For Infinite Computations

We show that many classical decision problems about 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are $\Pi_2^1$-complete, hence located at the second level of the analytical hierarchy, and "highly undecidable". In particular, the universality problem, the inclusion problem, the equivalence problem, the determinizability problem, the complementability problem, and the unambiguity problem are all $\Pi_2^1$-complete for context-free omega-languages or for infinitary rational relations. Topological and arithmetical properties of 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are also highly undecidable. These very surprising results provide the first examples of highly undecidable problems about the behaviour of very simple finite machines like 1-counter automata or 2-tape automata.Comment: to appear in RAIRO-Theoretical Informatics and Application

When Are Two Workflows the Same?

In the area of workflow management, one is confronted with a large number of competing languages and the relations between them (e.g. relative expressiveness) are usually not clear. Moreover, even within the same language it is generally possible to express the same workflow in different ways, a feature known as variability. This paper aims at providing some of the formal groundwork for studying relative expressiveness and variability by defining notions of equivalence capturing different views on how workflow systems operate. Firstly, a notion of observational equivalence in the absence of silent steps is defined and related to classical bisimulation. Secondly, a number of equivalence notions in the presence of silent steps are defined. A distinction is made between the case where silent steps are visible (but not controllable) by the environment and the case where silent steps are not visible, i.e., there is an alternation between system events and environment interactions. It is shown that these notions of equivalence are different and do not coincide with classical notions of bisimulation with silent steps (e.g. weak and branching)

In the Maze of Data Languages

In data languages the positions of strings and trees carry a label from a finite alphabet and a data value from an infinite alphabet. Extensions of automata and logics over finite alphabets have been defined to recognize data languages, both in the string and tree cases. In this paper we describe and compare the complexity and expressiveness of such models to understand which ones are better candidates as regular models

Deciding subset relationship of co-inductively defined set constants

Static analysis of different non-strict functional programming languages makes use of set constants like Top, Inf, and Bot denoting all expressions, all lists without a last Nil as tail, and all non-terminating programs, respectively. We use a set language that permits union, constructors and recursive definition of set constants with a greatest fixpoint semantics. This paper proves decidability, in particular EXPTIMEcompleteness, of subset relationship of co-inductively defined sets by using algorithms and results from tree automata. This shows decidability of the test for set inclusion, which is required by certain strictness analysis algorithms in lazy functional programming languages

Mean-payoff Automaton Expressions

Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating mean-payoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by mean-payoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Mean-payoff automaton expressions subsume deterministic mean-payoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating mean-payoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as mean-payoff automaton expressions

A Grammatical Inference Approach to Language-Based Anomaly Detection in XML

False-positives are a problem in anomaly-based intrusion detection systems. To counter this issue, we discuss anomaly detection for the eXtensible Markup Language (XML) in a language-theoretic view. We argue that many XML-based attacks target the syntactic level, i.e. the tree structure or element content, and syntax validation of XML documents reduces the attack surface. XML offers so-called schemas for validation, but in real world, schemas are often unavailable, ignored or too general. In this work-in-progress paper we describe a grammatical inference approach to learn an automaton from example XML documents for detecting documents with anomalous syntax. We discuss properties and expressiveness of XML to understand limits of learnability. Our contributions are an XML Schema compatible lexical datatype system to abstract content in XML and an algorithm to learn visibly pushdown automata (VPA) directly from a set of examples. The proposed algorithm does not require the tree representation of XML, so it can process large documents or streams. The resulting deterministic VPA then allows stream validation of documents to recognize deviations in the underlying tree structure or datatypes.Comment: Paper accepted at First Int. Workshop on Emerging Cyberthreats and Countermeasures ECTCM 201

The Wadge Hierarchy of Deterministic Tree Languages

We provide a complete description of the Wadge hierarchy for deterministically recognisable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to another. This extends Wagner's results on the hierarchy of omega-regular languages of words to the case of trees.Comment: 44 pages, 8 figures; extended abstract presented at ICALP 2006, Venice, Italy; full version appears in LMCS special issu

The equivalence problem for LL- and LR-regular grammars

It will be shown that the equivalence problem for LL-regular grammars is decidable. Apart from extending the known result for LL(k) grammar equivalence to LLregular grammar equivalence, we obtain an alternative proof of the decidability of LL(k) equivalence. The equivalence prob]em for LL-regular grammars has been studied before, but not solved. Our proof that this equivalence problem is decidable is simple. However, this is mainly because we can reduce the problem to the equivalence problem for real-time strict deterministic grammlars, which is decidable