12 research outputs found
Transformational Verification of Linear Temporal Logic
We present a new method for verifying Linear Temporal
Logic (LTL) properties of finite state reactive systems based on logic programming and program transformation. We encode a finite state system and an LTL property which we want to verify as a logic program on infinite lists. Then we apply a verification method consisting of two steps. In the first step we transform the logic program that encodes the given system and the given property into a new program belonging to the class of the so-called linear monadic !-programs (which are stratified, linear recursive programs defining nullary predicates or unary predicates on infinite lists). This transformation is performed by applying rules that preserve correctness. In the second step we verify the property of interest by using suitable proof rules for linear monadic !-programs. These proof rules can be encoded as a logic program which always terminates, if evaluated by using tabled resolution. Although our method uses standard
program transformation techniques, the computational complexity of the derived verification algorithm is essentially the same as the one of the Lichtenstein-Pnueli algorithm [9], which uses sophisticated ad-hoc techniques
Model-checking Timed Temporal Logics
AbstractIn this paper, we present several timed extensions of temporal logics, that can be used for model-checking real-time systems. We give different formalisms and the corresponding decidability/complexity results. We also give intuition to explain these results
Monotonic Set-Extended Prefix Rewriting and Verification of Recursive Ping-Pong Protocols
Ping-pong protocols with recursive definitions of agents, but without any active intruder, are a Turing powerful model. We show that under the environment sensitive semantics (i.e. by adding an active intruder capable of storing all exchanged messages including full analysis and synthesis of messages) some verification problems become decidable. In particular we give an algorithm to decide control state reachability, a problem related to security properties like secrecy and authenticity. The proof is via a reduction to a new prefix rewriting model called Monotonic Set-extended Prefix rewriting (MSP). We demonstrate further applicability of the introduced model by encoding a fragment of the ccp (concurrent constraint programming) language into MSP
Minimization and Canonization of GFG Transition-Based Automata
While many applications of automata in formal methods can use
nondeterministic automata, some applications, most notably synthesis, need
deterministic or good-for-games(GFG) automata. The latter are nondeterministic
automata that can resolve their nondeterministic choices in a way that only
depends on the past. The minimization problem for deterministic B\"uchi and
co-B\"uchi word automata is NP-complete. In particular, no canonical minimal
deterministic automaton exists, and a language may have different minimal
deterministic automata. We describe a polynomial minimization algorithm for GFG
co-B\"uchi word automata with transition-based acceptance. Thus, a run is
accepting if it traverses a set of designated transitions only
finitely often. Our algorithm is based on a sequence of transformations we
apply to the automaton, on top of which a minimal quotient automaton is
defined. We use our minimization algorithm to show canonicity for
transition-based GFG co-B\"uchi word automata: all minimal automata have
isomorphic safe components (namely components obtained by restricting the
transitions to these not in ) and once we saturate the automata with
-transitions, we get full isomorphism.Comment: 28 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:2009.1088
Reasoning About Strategies: On the Model-Checking Problem
In open systems verification, to formally check for reliability, one needs an
appropriate formalism to model the interaction between agents and express the
correctness of the system no matter how the environment behaves. An important
contribution in this context is given by modal logics for strategic ability, in
the setting of multi-agent games, such as ATL, ATL\star, and the like.
Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which
we denote here by CHP-SL, with the aim of getting a powerful framework for
reasoning explicitly about strategies. CHP-SL is obtained by using first-order
quantifications over strategies and has been investigated in the very specific
setting of two-agents turned-based games, where a non-elementary model-checking
algorithm has been provided. While CHP-SL is a very expressive logic, we claim
that it does not fully capture the strategic aspects of multi-agent systems. In
this paper, we introduce and study a more general strategy logic, denoted SL,
for reasoning about strategies in multi-agent concurrent games. We prove that
SL includes CHP-SL, while maintaining a decidable model-checking problem. In
particular, the algorithm we propose is computationally not harder than the
best one known for CHP-SL. Moreover, we prove that such a problem for SL is
NonElementarySpace-hard. This negative result has spurred us to investigate
here syntactic fragments of SL, strictly subsuming ATL\star, with the hope of
obtaining an elementary model-checking problem. Among the others, we study the
sublogics SL[NG], SL[BG], and SL[1G]. They encompass formulas in a special
prenex normal form having, respectively, nested temporal goals, Boolean
combinations of goals and, a single goal at a time. About these logics, we
prove that the model-checking problem for SL[1G] is 2ExpTime-complete, thus not
harder than the one for ATL\star
Deciding Second-order Logics using Database Evaluation Techniques
We outline a novel technique that maps the satisfiability problems of
second-order logics, in particular WSnS (weak monadic second-order
logic with n successors), S1S (monadic second-order logic with one
successor), and of μ-calculus, to the problem of query evaluation
of Complex-value Datalog queries. In this dissertation, we propose
techniques that use database evaluation and optimization techniques
for automata-based decision procedures for the above logics. We show
how the use of advanced implementation techniques for Deductive
databases and for Logic Programs, in particular the use of tabling,
yields a considerable improvement in performance over more traditional
approaches. We also explore various optimizations of the proposed
technique, in particular we consider variants of tabling and goal
reordering. We then show that the decision problem for S1S can be
mapped to the problem of query evaluation of
Complex-value Datalog queries.
We explore optimizations that
can be applied to various types of formulas. Last, we propose
analogous techniques that allow us to approach μ-calculus
satisfiability problem in an incremental fashion and without the need
for re-computation. In addition, we outline a top-down evaluation
technique to drive our incremental procedure and propose heuristics
that guide the problem partitioning to reduce the size of the problems
that need to be solved