43 research outputs found
Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata
We study the bisimilarity problem for probabilistic pushdown automata (pPDA)
and subclasses thereof. Our definition of pPDA allows both probabilistic and
non-deterministic branching, generalising the classical notion of pushdown
automata (without epsilon-transitions). We first show a general
characterization of probabilistic bisimilarity in terms of two-player games,
which naturally reduces checking bisimilarity of probabilistic labelled
transition systems to checking bisimilarity of standard (non-deterministic)
labelled transition systems. This reduction can be easily implemented in the
framework of pPDA, allowing to use known results for standard
(non-probabilistic) PDA and their subclasses. A direct use of the reduction
incurs an exponential increase of complexity, which does not matter in deriving
decidability of bisimilarity for pPDA due to the non-elementary complexity of
the problem. In the cases of probabilistic one-counter automata (pOCA), of
probabilistic visibly pushdown automata (pvPDA), and of probabilistic basic
process algebras (i.e., single-state pPDA) we show that an implicit use of the
reduction can avoid the complexity increase; we thus get PSPACE, EXPTIME, and
2-EXPTIME upper bounds, respectively, like for the respective non-probabilistic
versions. The bisimilarity problems for OCA and vPDA are known to have matching
lower bounds (thus being PSPACE-complete and EXPTIME-complete, respectively);
we show that these lower bounds also hold for fully probabilistic versions that
do not use non-determinism
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science
Countdown games, and simulation on (succinct) one-counter nets
We answer an open complexity question by Hofman, Lasota, Mayr, Totzke (LMCS
2016) [HLMT16] for simulation preorder of succinct one-counter nets (i.e.,
one-counter automata with no zero tests where counter increments and decrements
are integers written in binary), by showing that all relations between
bisimulation equivalence and simulation preorder are EXPSPACE-hard for these
nets. We describe a reduction from reachability games whose
EXPSPACE-completeness in the case of succinct one-counter nets was shown by
Hunter [RP 2015], by using other results. We also provide a direct
self-contained EXPSPACE-completeness proof for a special case of such
reachability games, namely for a modification of countdown games that were
shown EXPTIME-complete by Jurdzinski, Sproston, Laroussinie [LMCS 2008]; in our
modification the initial counter value is not given but is freely chosen by the
first player. We also present a new simplified proof of the belt theorem that
gives a simple graphic presentation of simulation preorder on one-counter nets
and leads to a polynomial-space algorithm; it is an alternative to the proof
from [HLMT16].Comment: A part of this paper elaborates arxiv-paper 1801.01073 and the
related paper presented at Reachability Problems 201
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems
Model checking infinite-state systems: generic and specific approaches
Model checking is a fully-automatic formal verification method that has been extremely
successful in validating and verifying safety-critical systems in the past three
decades. In the past fifteen years, there has been a lot of work in extending many
model checking algorithms over finite-state systems to finitely representable infinitestate
systems. Unlike in the case of finite systems, decidability can easily become a
problem in the case of infinite-state model checking.
In this thesis, we present generic and specific techniques that can be used to derive
decidability with near-optimal computational complexity for various model checking
problems over infinite-state systems. Generic techniques and specific techniques primarily
differ in the way in which a decidability result is derived. Generic techniques is
a “top-down” approach wherein we start with a Turing-powerful formalismfor infinitestate
systems (in the sense of being able to generate the computation graphs of Turing
machines up to isomorphisms), and then impose semantic restrictions whereby the
desired model checking problem becomes decidable. In other words, to show that a
subclass of the infinite-state systems that is generated by this formalism is decidable
with respect to the model checking problem under consideration, we will simply have
to prove that this subclass satisfies the semantic restriction. On the other hand, specific
techniques is a “bottom-up” approach in the sense that we restrict to a non-Turing
powerful formalism of infinite-state systems at the outset. The main benefit of generic
techniques is that they can be used as algorithmic metatheorems, i.e., they can give
unified proofs of decidability of various model checking problems over infinite-state
systems. Specific techniques are more flexible in the sense they can be used to derive
decidability or optimal complexity when generic techniques fail.
In the first part of the thesis, we adopt word/tree automatic transition systems as
a generic formalism of infinite-state systems. Such formalisms can be used to generate
many interesting classes of infinite-state systems that have been considered in the
literature, e.g., the computation graphs of counter systems, Turing machines, pushdown
systems, prefix-recognizable systems, regular ground-tree rewrite systems, PAprocesses,
order-2 collapsible pushdown systems. Although the generality of these
formalisms make most interesting model checking problems (even safety) undecidable,
they are known to have nice closure and algorithmic properties. We use these
nice properties to obtain several algorithmic metatheorems over word/tree automatic
systems, e.g., for deriving decidability of various model checking problems including
recurrent reachability, and Linear Temporal Logic (LTL) with complex fairness constraints. These algorithmic metatheorems can be used to uniformly prove decidability
with optimal (or near-optimal) complexity of various model checking problems over
many classes of infinite-state systems that have been considered in the literature. In
fact, many of these decidability/complexity results were not previously known in the
literature.
In the second part of the thesis, we study various model checking problems over
subclasses of counter systems that were already known to be decidable. In particular,
we consider reversal-bounded counter systems (and their extensions with discrete
clocks), one-counter processes, and networks of one-counter processes. We shall derive
optimal complexity of various model checking problems including: model checking
LTL, EF-logic, and first-order logic with reachability relations (and restrictions
thereof). In most cases, we obtain a single/double exponential reduction in the previously
known upper bounds on the complexity of the problems