329 research outputs found
Beyond Language Equivalence on Visibly Pushdown Automata
We study (bi)simulation-like preorder/equivalence checking on the class of
visibly pushdown automata and its natural subclasses visibly BPA (Basic Process
Algebra) and visibly one-counter automata. We describe generic methods for
proving complexity upper and lower bounds for a number of studied preorders and
equivalences like simulation, completed simulation, ready simulation, 2-nested
simulation preorders/equivalences and bisimulation equivalence. Our main
results are that all the mentioned equivalences and preorders are
EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly
one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for
visibly one-counter automata improves also the previously known DP-hardness
results for ordinary one-counter automata and one-counter nets. Finally, we
study regularity checking problems for visibly pushdown automata and show that
they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC
A theory of normed simulations
In existing simulation proof techniques, a single step in a lower-level
specification may be simulated by an extended execution fragment in a
higher-level one. As a result, it is cumbersome to mechanize these techniques
using general purpose theorem provers. Moreover, it is undecidable whether a
given relation is a simulation, even if tautology checking is decidable for the
underlying specification logic. This paper introduces various types of normed
simulations. In a normed simulation, each step in a lower-level specification
can be simulated by at most one step in the higher-level one, for any related
pair of states. In earlier work we demonstrated that normed simulations are
quite useful as a vehicle for the formalization of refinement proofs via
theorem provers. Here we show that normed simulations also have pleasant
theoretical properties: (1) under some reasonable assumptions, it is decidable
whether a given relation is a normed forward simulation, provided tautology
checking is decidable for the underlying logic; (2) at the semantic level,
normed forward and backward simulations together form a complete proof method
for establishing behavior inclusion, provided that the higher-level
specification has finite invisible nondeterminism.Comment: 31 pages, 10figure
Advanced Automata Minimization
We present an efficient algorithm to reduce the size of nondeterministic
Buchi word automata, while retaining their language. Additionally, we describe
methods to solve PSPACE-complete automata problems like universality,
equivalence and inclusion for much larger instances (1-3 orders of magnitude)
than before. This can be used to scale up applications of automata in formal
verification tools and decision procedures for logical theories. The algorithm
is based on new transition pruning techniques. These use criteria based on
combinations of backward and forward trace inclusions. Since these relations
are themselves PSPACE-complete, we describe methods to compute good
approximations of them in polynomial time. Extensive experiments show that the
average-case complexity of our algorithm scales quadratically. The size
reduction of the automata depends very much on the class of instances, but our
algorithm consistently outperforms all previous techniques by a wide margin. We
tested our algorithm on Buchi automata derived from LTL-formulae, many classes
of random automata and automata derived from mutual exclusion protocols, and
compared its performance to the well-known automata tool GOAL.Comment: 15 page
Generalized Strong Preservation by Abstract Interpretation
Standard abstract model checking relies on abstract Kripke structures which
approximate concrete models by gluing together indistinguishable states, namely
by a partition of the concrete state space. Strong preservation for a
specification language L encodes the equivalence of concrete and abstract model
checking of formulas in L. We show how abstract interpretation can be used to
design abstract models that are more general than abstract Kripke structures.
Accordingly, strong preservation is generalized to abstract
interpretation-based models and precisely related to the concept of
completeness in abstract interpretation. The problem of minimally refining an
abstract model in order to make it strongly preserving for some language L can
be formulated as a minimal domain refinement in abstract interpretation in
order to get completeness w.r.t. the logical/temporal operators of L. It turns
out that this refined strongly preserving abstract model always exists and can
be characterized as a greatest fixed point. As a consequence, some well-known
behavioural equivalences, like bisimulation, simulation and stuttering, and
their corresponding partition refinement algorithms can be elegantly
characterized in abstract interpretation as completeness properties and
refinements
On the Complexity of Deciding Behavioural Equivalences and Preorders. A Survey
This paper gives an overview of the computational complexity of all the equivalences in the linear/branching time hierarchy [vG90a] and the preordersin the corresponding hierarchy of preorders. We consider finite state or regular processes as well as infinite-state BPA [BK84b] processes. A distinction, which turns out to be important in the finite-state processes, is that of simulation-like equivalences/preorders vs. trace-like equivalencesand preorders. Here we survey various known complexity results for these relations. For regular processes, all simulation-like equivalences and preorders are decidable in polynomial time whereas all trace-like equivalences and preorders are PSPACE-Complete. We also consider interesting specialclasses of regular processes such as deterministic, determinate, unary, locally unary, and tree-like processes and survey the known complexity results inthese special cases. For infinite-state processes the results are quite different. For the class of context-free processes or BPA processes any preorder or equivalence beyond bisimulation is undecidable but bisimulation equivalence is polynomial timedecidable for normed BPA processes and is known to be elementarily decidable in the general case. For the class of BPP processes, all preorders and equivalences apart from bisimilarity are undecidable. However, bisimilarityis decidable in this case and is known to be decidable in polynomial time for normed BPP processes
Buffered Simulation Games for B\"uchi Automata
Simulation relations are an important tool in automata theory because they
provide efficiently computable approximations to language inclusion. In recent
years, extensions of ordinary simulations have been studied, for instance
multi-pebble and multi-letter simulations which yield better approximations and
are still polynomial-time computable.
In this paper we study the limitations of approximating language inclusion in
this way: we introduce a natural extension of multi-letter simulations called
buffered simulations. They are based on a simulation game in which the two
players share a FIFO buffer of unbounded size. We consider two variants of
these buffered games called continuous and look-ahead simulation which differ
in how elements can be removed from the FIFO buffer. We show that look-ahead
simulation, the simpler one, is already PSPACE-hard, i.e. computationally as
hard as language inclusion itself. Continuous simulation is even EXPTIME-hard.
We also provide matching upper bounds for solving these games with infinite
state spaces.Comment: In Proceedings AFL 2014, arXiv:1405.527
Using higher-order contracts to model session types
Session types are used to describe and structure interactions between
independent processes in distributed systems. Higher-order types are needed in
order to properly structure delegation of responsibility between processes.
In this paper we show that higher-order web-service contracts can be used to
provide a fully-abstract model of recursive higher-order session types. The
model is set-theoretic, in the sense that the meaning of a contract is given in
terms of the set of contracts with which it complies.
The proof of full-abstraction depends on a novel notion of the complement of
a contract. This in turn gives rise to an alternative to the type duality
commonly used in systems for type-checking session types. We believe that the
notion of complement captures more faithfully the behavioural intuition
underlying type duality.Comment: Added definitions of m-closed terms, of 'dual', and a discussion to
show the problems of the complement functio
Applicability of fair simulation
AbstractIn this paper we compare four notions of fair simulation: direct [9], delay [12], game [19], and exists [16]. Our comparison refers to three main aspects: The time complexity of constructing the fair simulation, the ability to use it for minimization, and the relationship between the fair simulations and universal branching-time logics. We developed a practical application that is based on this comparison. The application is a new implementation for the assume-guarantee modular framework presented By Grumberg at al. in [ACM Transactions on Programming Languages and Systems (TOPLAS), 16 (1994) 843]. The new implementation significantly improves the complexity of the framework
When are prime formulae characteristic?
In the setting of the modal logic that characterizes modal refinement over modal transition systems, Boudol and Larsen showed that the formulae for which model checking can be reduced to preorder checking, that is, the characteristic formulae, are exactly the consistent and prime ones. This paper presents general, sufficient conditions guaranteeing that characteristic formulae are exactly the consistent and prime ones. It is shown that the given conditions apply to the logics characterizing all the semantics in van Glabbeek's branching-time spectrum
- …