89 research outputs found
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
Algebraic properties of structured context-free languages: old approaches and novel developments
The historical research line on the algebraic properties of structured CF
languages initiated by McNaughton's Parenthesis Languages has recently
attracted much renewed interest with the Balanced Languages, the Visibly
Pushdown Automata languages (VPDA), the Synchronized Languages, and the
Height-deterministic ones. Such families preserve to a varying degree the basic
algebraic properties of Regular languages: boolean closure, closure under
reversal, under concatenation, and Kleene star. We prove that the VPDA family
is strictly contained within the Floyd Grammars (FG) family historically known
as operator precedence. Languages over the same precedence matrix are known to
be closed under boolean operations, and are recognized by a machine whose pop
or push operations on the stack are purely determined by terminal letters. We
characterize VPDA's as the subclass of FG having a peculiarly structured set of
precedence relations, and balanced grammars as a further restricted case. The
non-counting invariance property of FG has a direct implication for VPDA too.Comment: Extended version of paper presented at WORDS2009, Salerno,Italy,
September 200
Precedence Automata and Languages
Operator precedence grammars define a classical Boolean and deterministic
context-free family (called Floyd languages or FLs). FLs have been shown to
strictly include the well-known visibly pushdown languages, and enjoy the same
nice closure properties. We introduce here Floyd automata, an equivalent
operational formalism for defining FLs. This also permits to extend the class
to deal with infinite strings to perform for instance model checking.Comment: Extended version of the paper which appeared in Proceedings of CSR
2011, Lecture Notes in Computer Science, vol. 6651, pp. 291-304, 2011.
Theorem 1 has been corrected and a complete proof is given in Appendi
Non-null Infinitesimal Micro-steps: a Metric Temporal Logic Approach
Many systems include components interacting with each other that evolve with
possibly very different speeds. To deal with this situation many formal models
adopt the abstraction of "zero-time transitions", which do not consume time.
These however have several drawbacks in terms of naturalness and logic
consistency, as a system is modeled to be in different states at the same time.
We propose a novel approach that exploits concepts from non-standard analysis
to introduce a notion of micro- and macro-steps in an extension of the TRIO
metric temporal logic, called X-TRIO. We use X-TRIO to provide a formal
semantics and an automated verification technique to Stateflow-like notations
used in the design of flexible manufacturing systems.Comment: 20 pages, 2 figures, submitted to the conference "FORMATS: Formal
Modelling and Analysis of Timed Systems" 201
Cyclic Operator Precedence Grammars for Parallel Parsing
Operator precedence languages (OPL) enjoy the local parsability property,
which essentially means that a code fragment enclosed within a pair of markers
-- playing the role of parentheses -- can be compiled with no knowledge of its
external context. Such a property has been exploited to build parallel
compilers for languages formalized as OPLs. It has been observed, however, that
when the syntax trees of the sentences have a linear substructure, its parsing
must necessarily proceed sequentially making it impossible to split such a
subtree into chunks to be processed in parallel. Such an inconvenience is due
to the fact that so far much literature on OPLs has assumed the hypothesis that
equality precedence relation cannot be cyclic. This hypothesis was motivated by
the need to keep the mathematical notation as simple as possible.
We present an enriched version of operator precedence grammars, called
cyclic, that allows to use a simplified version of regular expressions in the
right hand sides of grammar's rules; for this class of operator precedence
grammars the acyclicity hypothesis of the equality precedence relation is no
more needed to guarantee the algebraic properties of the generated languages.
The expressive power of the cyclic grammars is now fully equivalent to that of
other formalisms defining OPLs such as operator precedence automata, monadic
second order logic and operator precedence expressions. As a result cyclic
operator precedence grammars now produce also unranked syntax trees and
sentences with flat unbounded substructures that can be naturally partitioned
into chunks suitable for parallel parsing.Comment: 23 pages, 8 figures. arXiv admin note: text overlap with
arXiv:2006.0123
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
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
SAFER-HRC: Safety analysis through formal vERification in human-robot collaboration
Whereas in classic robotic applications there is a clear segregation between robots and operators, novel robotic and cyber-physical systems have evolved in size and functionality to include the collaboration with human operators within common workspaces. This new application field, often referred to as Human-Robot Collaboration (HRC), raises new challenges to guarantee system safety, due to the presence of operators. We present an innovative methodology, called SAFER-HRC, centered around our logic language TRIO and the companion bounded satisfiability checker Zot, to assess the safety risks in an HRC application. The methodology starts from a generic modular model and customizes it for the target system; it then analyses hazards according to known standards, to study the safety of the collaborative environment
A temporal logic for micro- and macro-step-based real-time systems: Foundations and applications
Many systems include components interacting with each other that evolve at possibly very different speeds. To deal with this situation many formal models adopt the abstraction of “zero-time transitions”, which do not consume time. These, however, have several drawbacks in terms of naturalness and logic consistency, as a system is modeled to be in different states at the same time. We propose a novel approach that exploits concepts from non-standard analysis and pairs them with the traditional “next” operator of temporal logic to introduce a notion of micro- and macro-steps; our approach is enacted in an extension of the TRIO metric temporal logic, called X-TRIO. We study the expressiveness and decidability properties of the new logic. Decidability is achieved through translation of a meaningful subset of X-TRIO into Linear Temporal Logic, a traditional way to support automated verification. We illustrate the usefulness and the generality of our approach by applying it to provide a formal semantics of timed Petri nets, which allows for their automated verification. We also give an overview of a formal semantics of Stateflow/Simulink diagrams, defined in terms of X-TRIO, which has been applied to the automated verification of a robotic cell
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