Decision problems for Clark-congruential languages

A common question when studying a class of context-free grammars is whether equivalence is decidable within this class. We answer this question positively for the class of Clark-congruential grammars, which are of interest to grammatical inference. We also consider the problem of checking whether a given CFG is Clark-congruential, and show that it is decidable given that the CFG is a DCFG.Comment: Version 2 incorporates revisions prompted by the comments of anonymous referees at ICGI and LearnAu

Nonterminal Separating Macro Grammars

We extend the concept of nonterminal separating (or NTS) context-free grammar to nonterminal separating $m$-macro grammar where the mode of derivation $m$ is equal to "unrestricted". "outside-in' or "inside-out". Then we show some (partial) characterization results for these NTS $m$-macro grammars

The Inclusion Problem for Some Subclasses of Context-Free Languages

AbstractBy 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(D1)⊆L(D2)?” where D1 and D2 are taken from possibly different descriptor families of subclasses of context-free languages

Decision problems for Clark-congruential languages

A common question when studying a class of context-free grammars (CFGs) is whether equivalence is decidable within this class. We answer this question positively for the class of Clark-congruential grammars, which are of interest to grammatical inference. We also consider the problem of checking whether a given CFG is Clark-congruential, and show that it is decidable given that the CFG is a deterministic CFG

Toward a theory of input-driven locally parsable languages

If a context-free language enjoys the local parsability property then, no matter how the source string is segmented, each segment can be parsed independently, and an efficient parallel parsing algorithm becomes possible. The new class of locally chain parsable languages (LCPLs), included in the deterministic context-free language family, is here defined by means of the chain-driven automaton and characterized by decidable properties of grammar derivations. Such automaton decides whether to reduce or not a substring in a way purely driven by the terminal characters, thus extending the well-known concept of input-driven (ID) alias visibly pushdown machines. The LCPL family extends and improves the practically relevant Floyd's operator-precedence (OP) languages which are known to strictly include the ID languages, and for which a parallel-parser generator exists

Verification of Well-Structured Graph Transformation Systems

The aim of this thesis is the definition of a high-level framework for verifying concurrent and distributed systems. Verification in computer science is challenging, since models that are sufficiently expressive to describe real-life case studies suffer from the undecidability of interesting problems. This also holds for the graph transformation systems used in this thesis. To still be able to analyse these system we have to restrict either the class of systems we can model, the class of states we can express or the properties we can verify. In fact, in the framework we will present, all these limitations are possible and each allows to solve different verification problems. For modelling we use graphs as the states of the system and graph transformation rules to model state changes. More precisely, we use hypergraphs, where an edge may be incident to an arbitrary long sequence of nodes. As rule formalism we use the single pushout approach based on category theory. This provides us with a powerful formalisms that allows us to use a finite set of rules to describe an infinite transition system. To obtain decidability results while still maintaining an infinite state space we use the theory of well-structured transition systems (WSTS), the main source of decidability results in the infinite case. We need to equip our state space with a well-quasi-order (wqo) which is a simulation relation for the transition relation (this is also known as compatibility condition or monotonicity requirement). If a system can be seen as a WSTS and some additional conditions are satisfied, one can decide the coverability problem, i.e., the problem of verifying whether, from a given initial state one can reach a state that covers a final state, i.e. is larger than the final state with respect to a chosen order. This problem can be used for verification by giving a finite set of minimal error states that represent an infinite class of erroneous states (i.e. all larger states). By checking whether one of these minimal states is coverable, we verify whether an error is reachable. The theory of WSTS provides us with a generic backwards algorithm to solve this problem. For graphs we will introduce three orders, the minor ordering, the subgraph ordering and the induced subgraph ordering, and investigate which graph transformation systems form WSTS with these orders. Since only the minor ordering is a wqo on all graphs, we will first define so-called Q-restricted WSTS, where we only require that the chosen order is a wqo on the downward-closed class Q. We examine how this affects the decidability of the coverability problem and present appropriate classes Q such that the subgraph ordering and induced subgraph ordering form Q-restricted WSTS. Furthermore, we will prove the computability of the backward algorithm for these Q-restricted WSTS. More precisely, we will do this in the form of a framework and give necessary conditions for orders to be compatible with this framework. For the three mentioned orders we prove that they satisfy these conditions. Being compatible with different orders strengthens the framework in the following way: On the one hand error specifications have to be invariant wrt. the order, meaning that different orders can describe different properties. On the other hand, there is the following trade-off: coarser orders are wqos on larger sets of graphs, but fewer GTS are well-structured wrt. coarse orders (analogously the reverse holds for fine orders). Finally, we will present the tool Uncover which implements most of the theoretical framework defined in this thesis. The practical value of our approach is illustrated by several case studies and runtime results

Dynamic Protocol Reverse Engineering a Grammatical Inference Approach

Round trip engineering of software from source code and reverse engineering of software from binary files have both been extensively studied and the state-of-practice have documented tools and techniques. Forward engineering of protocols has also been extensively studied and there are firmly established techniques for generating correct protocols. While observation of protocol behavior for performance testing has been studied and techniques established, reverse engineering of protocol control flow from observations of protocol behavior has not received the same level of attention. State-of-practice in reverse engineering the control flow of computer network protocols is comprised of mostly ad hoc approaches. We examine state-of-practice tools and techniques used in three open source projects: Pidgin, Samba, and rdesktop . We examine techniques proposed by computational learning researchers for grammatical inference. We propose to extend the state-of-art by inferring protocol control flow using grammatical inference inspired techniques to reverse engineer automata representations from captured data flows. We present evidence that grammatical inference is applicable to the problem domain under consideration

Equational and membership constraints for infinite trees

We present a new constraint system with equational and membership constraints over infinite trees. It provides for complete and correct satisfiability and entailment tests and ir therefore suitable for the use in concurrent constraint programming systems which are based on cyclic data structures. Our set defining devices are greatest fixpoint solutions of regular systems of equations with a deterministic form of union. As the main technical particularity of the algorithms we present a novel memorization technique. We believe that both satisfiability and entailment tests can be implemented in an efficient and incremental manner

IST Austria Thesis

Motivated by the analysis of highly dynamic message-passing systems, i.e. unbounded thread creation, mobility, etc. we present a framework for the analysis of depth-bounded systems. Depth-bounded systems are one of the most expressive known fragment of the π-calculus for which interesting verification problems are still decidable. Even though they are infinite state systems depth-bounded systems are well-structured, thus can be analyzed algorithmically. We give an interpretation of depth-bounded systems as graph-rewriting systems. This gives more flexibility and ease of use to apply depth-bounded systems to other type of systems like shared memory concurrency. First, we develop an adequate domain of limits for depth-bounded systems, a prerequisite for the effective representation of downward-closed sets. Downward-closed sets are needed by forward saturation-based algorithms to represent potentially infinite sets of states. Then, we present an abstract interpretation framework to compute the covering set of well-structured transition systems. Because, in general, the covering set is not computable, our abstraction over-approximates the actual covering set. Our abstraction captures the essence of acceleration based-algorithms while giving up enough precision to ensure convergence. We have implemented the analysis in the PICASSO tool and show that it is accurate in practice. Finally, we build some further analyses like termination using the covering set as starting point

The word problem and combinatorial methods for groups and semigroups

The subject matter of this thesis is combinatorial semigroup theory. It includes material, in no particular order, from combinatorial and geometric group theory, formal language theory, theoretical computer science, the history of mathematics, formal logic, model theory, graph theory, and decidability theory. In Chapter 1, we will give an overview of the mathematical background required to state the results of the remaining chapters. The only originality therein lies in the exposition of special monoids presented in §1.3, which uni.es the approaches by several authors. In Chapter 2, we introduce some general algebraic and language-theoretic constructions which will be useful in subsequent chapters. As a corollary of these general methods, we recover and generalise a recent result by Brough, Cain & Pfei.er that the class of monoids with context-free word problem is closed under taking free products. In Chapter 3, we study language-theoretic and algebraic properties of special monoids, and completely classify this theory in terms of the group of units. As a result, we generalise the Muller-Schupp theorem to special monoids, and answer a question posed by Zhang in 1992. In Chapter 4, we give a similar treatment to weakly compressible monoids, and characterise their language-theoretic properties. As a corollary, we deduce many new results for one-relation monoids, including solving the rational subset membership problem for many such monoids. We also prove, among many other results, that it is decidable whether a one-relation monoid containing a non-trivial idempotent has context-free word problem. In Chapter 5, we study context-free graphs, and connect the algebraic theory of special monoids with the geometric behaviour of their Cayley graphs. This generalises the geometric aspects of the Muller-Schupp theorem for groups to special monoids. We study the growth rate of special monoids, and prove that a special monoid of intermediate growth is a group