787 research outputs found
Constraint LTL Satisfiability Checking without Automata
This paper introduces a novel technique to decide the satisfiability of
formulae written in the language of Linear Temporal Logic with Both future and
past operators and atomic formulae belonging to constraint system D (CLTLB(D)
for short). The technique is based on the concept of bounded satisfiability,
and hinges on an encoding of CLTLB(D) formulae into QF-EUD, the theory of
quantifier-free equality and uninterpreted functions combined with D. Similarly
to standard LTL, where bounded model-checking and SAT-solvers can be used as an
alternative to automata-theoretic approaches to model-checking, our approach
allows users to solve the satisfiability problem for CLTLB(D) formulae through
SMT-solving techniques, rather than by checking the emptiness of the language
of a suitable automaton A_{\phi}. The technique is effective, and it has been
implemented in our Zot formal verification tool.Comment: 39 page
On Relaxing Metric Information in Linear Temporal Logic
Metric LTL formulas rely on the next operator to encode time distances,
whereas qualitative LTL formulas use only the until operator. This paper shows
how to transform any metric LTL formula M into a qualitative formula Q, such
that Q is satisfiable if and only if M is satisfiable over words with
variability bounded with respect to the largest distances used in M (i.e.,
occurrences of next), but the size of Q is independent of such distances.
Besides the theoretical interest, this result can help simplify the
verification of systems with time-granularity heterogeneity, where large
distances are required to express the coarse-grain dynamics in terms of
fine-grain time units.Comment: Minor change
Linear Encodings of Bounded LTL Model Checking
We consider the problem of bounded model checking (BMC) for linear temporal
logic (LTL). We present several efficient encodings that have size linear in
the bound. Furthermore, we show how the encodings can be extended to LTL with
past operators (PLTL). The generalised encoding is still of linear size, but
cannot detect minimal length counterexamples. By using the virtual unrolling
technique minimal length counterexamples can be captured, however, the size of
the encoding is quadratic in the specification. We also extend virtual
unrolling to Buchi automata, enabling them to accept minimal length
counterexamples.
Our BMC encodings can be made incremental in order to benefit from
incremental SAT technology. With fairly small modifications the incremental
encoding can be further enhanced with a termination check, allowing us to prove
properties with BMC. Experiments clearly show that our new encodings improve
performance of BMC considerably, particularly in the case of the incremental
encoding, and that they are very competitive for finding bugs. An analysis of
the liveness-to-safety transformation reveals many similarities to the BMC
encodings in this paper. Using the liveness-to-safety translation with
BDD-based invariant checking results in an efficient method to find shortest
counterexamples that complements the BMC-based approach.Comment: Final version for Logical Methods in Computer Science CAV 2005
special issu
Deciding the Satisfiability of MITL Specifications
In this paper we present a satisfiability-preserving reduction from MITL
interpreted over finitely-variable continuous behaviors to Constraint LTL over
clocks, a variant of CLTL that is decidable, and for which an SMT-based bounded
satisfiability checker is available. The result is a new complete and effective
decision procedure for MITL. Although decision procedures for MITL already
exist, the automata-based techniques they employ appear to be very difficult to
realize in practice, and, to the best of our knowledge, no implementation
currently exists for them. A prototype tool for MITL based on the encoding
presented here has, instead, been implemented and is publicly available.Comment: In Proceedings GandALF 2013, arXiv:1307.416
Visibly Linear Dynamic Logic
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear
Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown
languages over finite words. In VLDL one can, e.g., express that a function
resets a variable to its original value after its execution, even in the
presence of an unbounded number of intermediate recursive calls. We prove that
VLDL describes exactly the -visibly pushdown languages. Thus it is
strictly more expressive than LTL and able to express recursive properties of
programs with unbounded call stacks.
The main technical contribution of this work is a translation of VLDL into
-visibly pushdown automata of exponential size via one-way alternating
jumping automata. This translation yields exponential-time algorithms for
satisfiability, validity, and model checking. We also show that visibly
pushdown games with VLDL winning conditions are solvable in triply-exponential
time. We prove all these problems to be complete for their respective
complexity classes.Comment: 25 Page
Structural Synthesis for GXW Specifications
We define the GXW fragment of linear temporal logic (LTL) as the basis for
synthesizing embedded control software for safety-critical applications. Since
GXW includes the use of a weak-until operator we are able to specify a number
of diverse programmable logic control (PLC) problems, which we have compiled
from industrial training sets. For GXW controller specifications, we develop a
novel approach for synthesizing a set of synchronously communicating
actor-based controllers. This synthesis algorithm proceeds by means of
recursing over the structure of GXW specifications, and generates a set of
dedicated and synchronously communicating sub-controllers according to the
formula structure. In a subsequent step, 2QBF constraint solving identifies and
tries to resolve potential conflicts between individual GXW specifications.
This structural approach to GXW synthesis supports traceability between
requirements and the generated control code as mandated by certification
regimes for safety-critical software. Synthesis for GXW specifications is in
PSPACE compared to 2EXPTIME-completeness of full-fledged LTL synthesis. Indeed
our experimental results suggest that GXW synthesis scales well to
industrial-sized control synthesis problems with 20 input and output ports and
beyond.Comment: The long (including appendix) version being reviewed by CAV'16
program committee. Compared to the submitted version, one author (out of her
wish) is moved to the Acknowledgement. (v2) Corrected typos. (v3) Add an
additional remark over environment assumption and easy corner case
- …