24 research outputs found
Guarded Second-Order Logic, Spanning Trees, and Network Flows
According to a theorem of Courcelle monadic second-order logic and guarded
second-order logic (where one can also quantify over sets of edges) have the
same expressive power over the class of all countable -sparse hypergraphs.
In the first part of the present paper we extend this result to hypergraphs of
arbitrary cardinality. In the second part, we present a generalisation dealing
with methods to encode sets of vertices by single vertices
Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems
Higher-order pushdown systems (PDSs) generalise pushdown systems through the
use of higher-order stacks, that is, a nested "stack of stacks" structure.
These systems may be used to model higher-order programs and are closely
related to the Caucal hierarchy of infinite graphs and safe higher-order
recursion schemes.
We consider the backwards-reachability problem over higher-order Alternating
PDSs (APDSs), a generalisation of higher-order PDSs. This builds on and extends
previous work on pushdown systems and context-free higher-order processes in a
non-trivial manner. In particular, we show that the set of configurations from
which a regular set of higher-order APDS configurations is reachable is regular
and computable in n-EXPTIME. In fact, the problem is n-EXPTIME-complete.
We show that this work has several applications in the verification of
higher-order PDSs, such as linear-time model-checking, alternation-free
mu-calculus model-checking and the computation of winning regions of
reachability games
The Hanoi Omega-Automata Format
We propose a flexible exchange format for Ï-automata, as typically used in formal verification, and implement support for it in a range of established tools. Our aim is to simplify the interaction of tools, helping the research community to build upon other peopleâs work. A key feature of the format is the use of very generic acceptance conditions, specified by Boolean combinations of acceptance primitives, rather than being limited to common cases such as BĂŒchi, Streett, or Rabin. Such flexibility in the choice of acceptance conditions can be exploited in applications, for example in probabilistic model checking, and furthermore encourages the development of acceptance-agnostic tools for automata manipulations. The format allows acceptance conditions that are either state-based or transition-based, and also supports alternating automata
Congruences for Visibly Pushdown Languages
We study congruences on words in order to characterize the class of visibly pushdown languages (VPL), a subclass of context-free languages. For any language L, we define a natural congruence on words that resembles the syntactic congruence for regular languages, such that this congruence is of finite index if, and only if, L is a VPL. We then study the problem of finding canonical minimal deterministic automata for VPLs. Though VPLs in general do not have a unique minimal automata, we show that the class of well-matched VPLs does have unique minimal k-module automata. We then present a minimization algorithm, which takes a k-module visibly pushdown automaton and constructs the minimal k-module machine for it in polynomial time
A Generalization of Semenov's Theorem to Automata over Real Numbers
peer reviewedInteruniversity Attraction Poles program MoVES; Grant 2.4530.02; ANR-06-SETI-001 AVERIS
Temporal Reasoning for Procedural Programs â
Abstract. While temporal verification of programs is a topic with a long history, its traditional basisâsemantics based on word languagesâis illsuited for modular reasoning about procedural programs. We address this issue by defining the semantics of procedural (potentially recursive) programs using languages of nested words and developing a framework for temporal reasoning around it. This generalization has two benefits. First, this style of reasoning naturally unifies Manna-Pnueli-style temporal reasoning with Hoare-style reasoning about structured programs. Second, it allows verification of ânon-regular â properties of specific procedural contextsâe.g., âIf a lock is acquired in a context, then it is released in the same context. â We present proof rules for a variety of properties such as local safety, local response, and staircase reactivity; our rules are sufficient to prove all temporal properties over nested words. We show that our rules are sound and relatively complete.