18,552 research outputs found
Pure-Past Linear Temporal and Dynamic Logic on Finite Traces
LTLf and LDLf are well-known logics on finite traces. We review PLTLf and PLDLf, their pure- past versions. These are interpreted backward from the end of the trace towards the beginning. Because of this, we can exploit a foundational result on reverse languages to get an exponential improvement, wrt LTLf /LDLf, in computing the corresponding DFA. This exponential improvement is reflected in several forms sequential decision making involving temporal specifications, such as planning and decision problems in non-deterministic and non-Markovian domains. Interestingly, PLTLf (resp. PLDLf ) has the same expressive power as LTLf (resp. LDLf ), but transforming a PLTLf (resp. PLDLf ) formula into its equivalent in LTLf (resp. LDLf ) is quite expensive. Hence, to take advantage of the exponential improvement, properties of interest must be directly expressed in PLTLf /PLTLf
Interestingness of traces in declarative process mining: The janus LTLPf Approach
Declarative process mining is the set of techniques aimed at extracting behavioural constraints from event logs. These constraints are inherently of a reactive nature, in that their activation restricts the occurrence of other activities. In this way, they are prone to the principle of ex falso quod libet: they can be satisfied even when not activated. As a consequence, constraints can be mined that are hardly interesting to users or even potentially misleading. In this paper, we build on the observation that users typically read and write temporal constraints as if-statements with an explicit indication of the activation condition. Our approach is called Janus, because it permits the specification and verification of reactive constraints that, upon activation, look forward into the future and backwards into the past of a trace. Reactive constraints are expressed using Linear-time Temporal Logic with Past on Finite Traces (LTLp f). To mine them out of event logs, we devise a time bi-directional valuation technique based on triplets of automata operating in an on-line fashion. Our solution proves efficient, being at most quadratic w.r.t. trace length, and effective in recognising interestingness of discovered constraints
LTL over Finite Words Can Be Exponentially More Succinct Than Pure-Past LTL, and vice versa
Linear Temporal Logic over finite traces (LTLf) has proved itself to be an important and effective formalism in formal verification as well as in artificial intelligence. Pure past LTLf (pLTL) is the logic obtained from LTLf by replacing each (future) temporal operator by a corresponding past one, and is naturally interpreted at the end of a finite trace. It is known that each property definable in LTLf is also definable in pLTL, and vice versa. However, despite being extensively used in practice, to the best of our knowledge, there is no systematic study of their succinctness. In this paper, we investigate the succinctness of LTLf and pLTL. First, we prove that pLTL can be exponentially more succinct than LTLf by showing that there exists a property definable with a pLTL formula of size n such that the size of all LTLf formulas defining it is at least exponential in n. Then, we prove that LTLf can be exponentially more succinct than pLTL as well. This result shows that, although being expressively equivalent, LTLf and pLTL are incomparable when succinctness is concerned. In addition, we study the succinctness of Safety-LTL (the syntactic safety fragment of LTL over infinite traces) with respect to its canonical form G(pLTL), whose formulas are of the form G(α), G being the globally operator and α a pLTL formula. We prove that G(pLTL) can be exponentially more succinct than Safety-LTL, and that the same holds for the dual cosafety fragment. 2012 ACM Subject Classification Theory of computation → Modal and temporal logics; Theory of computation → Logic and verificatio
A tool for declarative Trace Alignment via automated planning
We present a tool, called TraceAligner, for solving Trace Alignment by first compiling into Planning and then solving it with any available cost-optimal planner. TraceAligner can produce different variants of the output Planning instance, each offering different degrees of readability and solution efficiency. The Planning instance is expressed in PDDL, the Planning Domain Definition Language. The tool can be easily extended and coupled with any planner taking PDDL as input language. A thorough experimental analysis has shown that the approach dramatically outperforms existing ad-hoc tools, thus making TraceAligner the best-performing tool for Trace Alignment with declarative specifications
Past-present temporal programs over finite traces
Extensions of Answer Set Programming with language constructs from temporal
logics, such as temporal equilibrium logic over finite traces (TELf), provide
an expressive computational framework for modeling dynamic applications. In
this paper, we study the so-called past-present syntactic subclass, which
consists of a set of logic programming rules whose body references to the past
and head to the present. Such restriction ensures that the past remains
independent of the future, which is the case in most dynamic domains. We extend
the definitions of completion and loop formulas to the case of past-present
formulas, which allows capturing the temporal stable models of a set of
past-present temporal programs by means of an LTLf expression
SMT-based Verification of LTL Specifications with Integer Constraints and its Application to Runtime Checking of Service Substitutability
An important problem that arises during the execution of service-based
applications concerns the ability to determine whether a running service can be
substituted with one with a different interface, for example if the former is
no longer available. Standard Bounded Model Checking techniques can be used to
perform this check, but they must be able to provide answers very quickly, lest
the check hampers the operativeness of the application, instead of aiding it.
The problem becomes even more complex when conversational services are
considered, i.e., services that expose operations that have Input/Output data
dependencies among them. In this paper we introduce a formal verification
technique for an extension of Linear Temporal Logic that allows users to
include in formulae constraints on integer variables. This technique applied to
the substitutability problem for conversational services is shown to be
considerably faster and with smaller memory footprint than existing ones
FOND planning for pure-past linear temporal logic goals
Recently, Pure-Past Temporal Logic (PPLTL) has proven highly effective in specifying temporally extended goals in deterministic planning domains. In this paper, we show its effectiveness also for fully observable nondeterministic (FOND) planning, both for strong and strong-cyclic plans. We present a notably simple encoding of FOND planning for PPLTL goals into standard FOND planning for final-state goals. The encoding only introduces few fluents (at most linear in the PPLTL goal) without adding any spurious action and allows planners to lazily build the relevant part of the deterministic automaton for the goal formula on-the-fly during the search. We formally prove its correctness, implement it in a tool called Plan4Past, and experimentally show its practical effectiveness
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