Optimised determinisation and completion of finite tree automata

Determinisation and completion of finite tree automata are important operations with applications in program analysis and verification. However, the complexity of the classical procedures for determinisation and completion is high. They are not practical procedures for manipulating tree automata beyond very small ones. In this paper we develop an algorithm for determinisation and completion of finite tree automata, whose worst-case complexity remains unchanged, but which performs far better than existing algorithms in practice. The critical aspect of the algorithm is that the transitions of the determinised (and possibly completed) automaton are generated in a potentially very compact form called product form, which can reduce the size of the representation dramatically. Furthermore, the representation can often be used directly when manipulating the determinised automaton. The paper contains an experimental evaluation of the algorithm on a large set of tree automata examples

Learning probability distributions generated by finite-state machines

We review methods for inference of probability distributions generated by probabilistic automata and related models for sequence generation. We focus on methods that can be proved to learn in the inference in the limit and PAC formal models. The methods we review are state merging and state splitting methods for probabilistic deterministic automata and the recently developed spectral method for nondeterministic probabilistic automata. In both cases, we derive them from a high-level algorithm described in terms of the Hankel matrix of the distribution to be learned, given as an oracle, and then describe how to adapt that algorithm to account for the error introduced by a finite sample.Peer ReviewedPostprint (author's final draft

Finite Model Finding for Parameterized Verification

In this paper we investigate to which extent a very simple and natural "reachability as deducibility" approach, originated in the research in formal methods in security, is applicable to the automated verification of large classes of infinite state and parameterized systems. The approach is based on modeling the reachability between (parameterized) states as deducibility between suitable encodings of states by formulas of first-order predicate logic. The verification of a safety property is reduced to a pure logical problem of finding a countermodel for a first-order formula. The later task is delegated then to the generic automated finite model building procedures. In this paper we first establish the relative completeness of the finite countermodel finding method (FCM) for a class of parameterized linear arrays of finite automata. The method is shown to be at least as powerful as known methods based on monotonic abstraction and symbolic backward reachability. Further, we extend the relative completeness of the approach and show that it can solve all safety verification problems which can be solved by the traditional regular model checking.Comment: 17 pages, slightly different version of the paper is submitted to TACAS 201

Finite Models vs Tree Automata in Safety Verification

In this paper we deal with verification of safety properties of term-rewriting systems. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which is further resolved by a generic finite model finding procedure. A finite countermodel produced during successful verification provides with a concise description of the system invariant sufficient to demonstrate a specific safety property. We show the relative completeness of this approach with respect to the tree automata completion technique. On a set of examples taken from the literature we demonstrate the efficiency of finite model finding approach as well as its explanatory power

A UML-based static verification framework for security

Secure software engineering is a new research area that has been proposed to address security issues during the development of software systems. This new area of research advocates that security characteristics should be considered from the early stages of the software development life cycle and should not be added as another layer in the system on an ad-hoc basis after the system is built. In this paper, we describe a UML-based Static Verification Framework (USVF) to support the design and verification of secure software systems in early stages of the software development life-cycle taking into consideration security and general requirements of the software system. USVF performs static verification on UML models consisting of UML class and state machine diagrams extended by an action language. We present an operational semantics of UML models, define a property specification language designed to reason about temporal and general properties of UML state machines using the semantic domains of the former, and implement the model checking process by translating models and properties into Promela, the input language of the SPIN model checker. We show that the methodology can be applied to the verification of security properties by representing the main aspects of security, namely availability, integrity and confidentiality, in the USVF property specification language

Incremental Parser Generation for Tree Adjoining Grammars

This paper describes the incremental generation of parse tables for the LR-type parsing of Tree Adjoining Languages (TALs). The algorithm presented handles modifications to the input grammar by updating the parser generated so far. In this paper, a lazy generation of LR-type parsers for TALs is defined in which parse tables are created by need while parsing. We then describe an incremental parser generator for TALs which responds to modification of the input grammar by updating parse tables built so far.Comment: 12 pages, 12 Postscript figures, uses fullname.st