4,581 research outputs found
Temporal Logic and Model Checking for Operator Precedence Languages
In the last decades much research effort has been devoted to extending the
success of model checking from the traditional field of finite state machines
and various versions of temporal logics to suitable subclasses of context-free
languages and appropriate extensions of temporal logics. To the best of our
knowledge such attempts only covered structured languages, i.e. languages whose
structure is immediately "visible" in their sentences, such as tree-languages
or visibly pushdown ones. In this paper we present a new temporal logic
suitable to express and automatically verify properties of operator precedence
languages. This "historical" language family has been recently proved to enjoy
fundamental algebraic and logic properties that make it suitable for model
checking applications yet breaking the barrier of visible-structure languages
(in fact the original motivation of its inventor Floyd was just to support
efficient parsing, i.e. building the "hidden syntax tree" of language
sentences). We prove that our logic is at least as expressive as analogous
logics defined for visible pushdown languages yet covering a much more powerful
family; we design a procedure that, given a formula in our logic builds an
automaton recognizing the sentences satisfying the formula, whose size is at
most exponential in the length of the formula.Comment: In Proceedings GandALF 2018, arXiv:1809.0241
Aperiodicity, Star-freeness, and First-order Definability of Structured Context-Free Languages
A classic result in formal language theory is the equivalence among
noncounting, or aperiodic, regular languages, and languages defined through
star-free regular expressions, or first-order logic. Together with first-order
completeness of linear temporal logic these results constitute a theoretical
foundation for model-checking algorithms. Extending these results to structured
subclasses of context-free languages, such as tree-languages did not work as
smoothly: for instance W. Thomas showed that there are star-free tree languages
that are counting. We show, instead, that investigating the same properties
within the family of operator precedence languages leads to equivalences that
perfectly match those on regular languages. The study of this old family of
context-free languages has been recently resumed to enhance not only parsing
(the original motivation of its inventor R. Floyd) but also to exploit their
algebraic and logic properties. We have been able to reproduce the classic
results of regular languages for this much larger class by going back to string
languages rather than tree languages. Since operator precedence languages
strictly include other classes of structured languages such as visibly pushdown
languages, the same results given in this paper hold as trivial corollary for
that family too
A First-Order Complete Temporal Logic for Structured Context-Free Languages
The problem of model checking procedural programs has fostered much research
towards the definition of temporal logics for reasoning on context-free
structures. The most notable of such results are temporal logics on Nested
Words, such as CaRet and NWTL. Recently, the logic OPTL was introduced, based
on the class of Operator Precedence Languages (OPLs), more powerful than Nested
Words. We define the new OPL-based logic POTL and prove its FO-completeness.
POTL improves on NWTL by enabling the formulation of requirements involving
pre/post-conditions, stack inspection, and others in the presence of
exception-like constructs. It improves on OPTL too, which instead we show not
to be FO-complete; it also allows to express more easily stack inspection and
function-local properties. In a companion paper we report a model checking
procedure for POTL and experimental results based on a prototype tool developed
therefor. For completeness a short summary of this complementary result is
provided in this paper too.Comment: Partially supersedes arXiv:1910.0932
A First-Order Complete Temporal Logic for Structured Context-Free Languages
The problem of model checking procedural programs has fostered much research
towards the definition of temporal logics for reasoning on context-free
structures. The most notable of such results are temporal logics on Nested
Words, such as CaRet and NWTL. Recently, the logic OPTL was introduced, based
on the class of Operator Precedence Languages (OPLs), more powerful than Nested
Words. We define the new OPL-based logic POTL and prove its FO-completeness.
POTL improves on NWTL by enabling the formulation of requirements involving
pre/post-conditions, stack inspection, and others in the presence of
exception-like constructs. It improves on OPTL too, which instead we show not
to be FO-complete; it also allows to express more easily stack inspection and
function-local properties. In a companion paper we report a model checking
procedure for POTL and experimental results based on a prototype tool developed
therefor. For completeness a short summary of this complementary result is
provided in this paper too
Events in Property Patterns
A pattern-based approach to the presentation, codification and reuse of
property specifications for finite-state verification was proposed by Dwyer and
his collegues. The patterns enable non-experts to read and write formal
specifications for realistic systems and facilitate easy conversion of
specifications between formalisms, such as LTL, CTL, QRE. In this paper, we
extend the pattern system with events - changes of values of variables in the
context of LTL.Comment: 14 pages, 3 figure
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
Generalizing input-driven languages: theoretical and practical benefits
Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks
to their simplicity they enjoy various nice algebraic and logic properties that
have been successfully exploited in many application fields. Practically all of
their related problems are decidable, so that they support automatic
verification algorithms. Also, they can be recognized in real-time.
Context-free languages (CFL) are another major family well-suited to
formalize programming, natural, and many other classes of languages; their
increased generative power w.r.t. RL, however, causes the loss of several
closure properties and of the decidability of important problems; furthermore
they need complex parsing algorithms. Thus, various subclasses thereof have
been defined with different goals, spanning from efficient, deterministic
parsing to closure properties, logic characterization and automatic
verification techniques.
Among CFL subclasses, so-called structured ones, i.e., those where the
typical tree-structure is visible in the sentences, exhibit many of the
algebraic and logic properties of RL, whereas deterministic CFL have been
thoroughly exploited in compiler construction and other application fields.
After surveying and comparing the main properties of those various language
families, we go back to operator precedence languages (OPL), an old family
through which R. Floyd pioneered deterministic parsing, and we show that they
offer unexpected properties in two fields so far investigated in totally
independent ways: they enable parsing parallelization in a more effective way
than traditional sequential parsers, and exhibit the same algebraic and logic
properties so far obtained only for less expressive language families
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