Massimo Cairo

A Streamlined Model of Conditional Simple Temporal Networks - Semantics and Equivalence Results.

A Conditional Simple Temporal Network (CSTN) augments a Simple Temporal Network to include a new kind of time-point, called an observation time-point. The execution of an observation time-point generates information in real time, specifically, the truth value of a propositional letter. In addition, time-points and temporal constraints may be labeled by conjunctions of (positive or negative) propositional letters. A CSTN is called dynamically consistent (DC) if there exists a dynamic strategy for executing its time-points such that no matter how the observations turn out during execution, the time-points whose labels are consistent with those observations have all been executed, and the constraints whose labels are consistent with those observations have all been satisfied. The strategy is dynamic in that its execution decisions may react to observations. The original formulation of CSTNs included propositional labels only on time-points, but the DC-checking algorithm was impractical because it was based on a conversion of the semantic constraints into an exponentially-sized Disjunctive Temporal Network. Later work added propositional labels to temporal constraints, and yielded a sound-and-complete propagation-based DC-checking algorithm, empirically demonstrated to be practical across a variety of CSTNs. This paper introduces a streamlined version of a CSTN in which propositional labels may appear on constraints, but not on time-points. This change simplifies the definition of the DC property, as well as the propagation rules for the DC-checking algorithm. It also simplifies the proofs of the soundness and completeness of those rules. This paper provides two translations from traditional CSTNs to streamlined CSTNs. Each translation preserves the DC property and, for any DC network, ensures that any dynamic execution strategy for that network can be extended to a strategy for its streamlined counterpart. Finally, this paper presents an empirical comparison of two versions of the DC-checking algorithm: the original version and a simplified version for streamlined CSTNs. The comparison is based on CSTN benchmarks from earlier work. For small-sized CSTNs, the original version shows the best performance, but the performance difference between the two versions decreases as the number of time-points in the CSTN increases. We conclude that the simplified algorithm is a practical alternative for checking the dynamic consistency of CSTNs. 1998 ACM Subject Classification G.2.2 Graph Theory, I.2.8 Problem Solving, Control Methods, and Search

Incorporating Decision Nodes into Conditional Simple Temporal Networks

A Conditional Simple Temporal Network (CSTN) augments a Simple Temporal Network (STN) to include special time-points, called observation time-points. In a CSTN, the agent executing the network controls the execution of every time-point. However, each observation time-point has a unique propositional letter associated with it and, when the agent executes that time-point, the environment assigns a truth value to the corresponding letter. Thus, the agent observes but, does not control the assignment of truth values. A CSTN is dynamically consistent (DC) if there exists a strategy for executing its time-points such that all relevant constraints will be satisfied no matter which truth values the environment assigns to the propositional letters. Alternatively, in a Labeled Simple Temporal Network (Labeled STN) - also called a Temporal Plan with Choice - the agent executing the network controls the assignment of values to the so-called choice variables. Furthermore, the agent can make those assignments at any time. For this reason, a Labeled STN is equivalent to a Disjunctive Temporal Network. This paper incorporates both of the above extensions by augmenting a CSTN to include not only observation time-points but also decision time-points. A decision time-point is like an observation time-point in that it has an associated propositional letter whose value is determined when the decision time-point is executed. It differs in that the agent - not the environment - selects that value. The resulting network is called a CSTN with Decisions (CSTND). This paper shows that a CSTND generalizes both CSTNs and Labeled STNs, and proves that the problem of determining whether any given CSTND is dynamically consistent is PSPACE-complete. It also presents algorithms that address two sub-classes of CSTNDs: (1) those that contain only decision time-points; and (2) those in which all decisions are made before execution begins.

Optimal Omnitig Listing for Safe and Complete Contig Assembly

Genome assembly is the problem of reconstructing a genome sequence from a set of reads from a sequencing experiment. Typical formulations of the assembly problem admit in practice many genomic reconstructions, and actual genome assemblers usually output contigs, namely substrings that are promised to occur in the genome. To bridge the theory and practice, Tomescu and Medvedev [RECOMB 2016] reformulated contig assembly as finding all substrings common to all genomic reconstructions. They also gave a characterization of those walks (omnitigs) that are common to all closed edge-covering walks of a (directed) graph, a typical notion of genomic reconstruction. An algorithm for listing all maximal omnitigs was also proposed, by launching an exhaustive visit from every edge. In this paper, we prove new insights about the structure of omnitigs and solve several open questions about them. We combine these to achieve an O(nm)-time algorithm for outputting all the maximal omnitigs of a graph (with n nodes and m edges). This is also optimal, as we show families of graphs whose total omnitig length is Omega(nm). We implement this algorithm and show that it is 9-12 times faster in practice than the one of Tomescu and Medvedev [RECOMB 2016].

Instantaneous Reaction-Time in Dynamic-Consistency Checking of Conditional Simple Temporal Networks

Conditional Simple Temporal Network CSTN is a constraint-based graph-formalism for conditional temporal planning. Three notions of consistency arise for CSTNs and CSTPs: weak, strong, and dynamic. Dynamic-Consistency (DC) is the most interesting notion, but it is also the most challenging. In order to address the DC-Checking problem, in [Comin and Rizzi, TIME 2015] we introduced ε-DC (a refined, more realistic, notion of DC), and provided an algorithmic solution to it. Next, given that DC implies ε-DC for some sufficiently small ε > 0, and that for every ε > 0 it holds that ε-DC implies DC, we offered a sharp lower bounding analysis on the critical value of the reaction-time ε under which the two notions coincide. This delivered the first (pseudo) singly-exponential time algorithm for the DC-Checking of CSTNs. However, the ε-DC notion is interesting per se, and the ε-DC-Checking algorithm in [Comin and Rizzi, TIME 2015] rests on the assumption that the reaction-time satisfies ε > 0, leaving unsolved the question of what happens when ε = 0. In this work, we introduce and study π-DC, a sound notion of DC with an instantaneous reaction-time (i.e. one in which the planner can react to any observation at the same instant of time in which the observation is made). Firstly, we demonstrate by a counter-example that π-DC is not equivalent to 0-DC, and that 0-DC is actually inadequate for modeling DC with an instantaneous reaction-time. This shows that the main results obtained in our previous work do not apply directly, as they were formulated, to the case of ε = 0. Motivated by this observation, as a second contribution, our previous tools are extended in order to handle π-DC, and the notion of ps-tree is introduced, also pointing out a relationship between π-DC and HyTN-Consistency. Thirdly, a simple reduction from π-DC-Checking to DC-Checking is identified. This allows us to design and to analyze the first sound-and-complete π-DC-Checking procedure. Remarkably, the time complexity of the proposed algorithm remains (pseudo) singly-exponential in the number of propositional letters.

The complexity of simulation and matrix multiplication

Computing the simulation preorder of a given Kripke structure (i.e., a directed graph with

Dynamic Controllability of Conditional Simple Temporal Networks Is PSPACE-complete

n

New bounds for approximating extremal distances in undirected graphs

labeled vertices) has crucial applications in model checking of temporal logic. It amounts to solving a specific two-players reachability game, called simulation game. We offer the first conditional lower bounds for this problem, and we relate its complexity (for computation, verification, and certification) to some variants of

Decoding Hidden Markov Models faster than viterbi via online matrix-vector (max, +)-multiplication

n\times n

Hardness of Covering Alignment: Phase Transition in Post-Sequence Genomics

matrix multiplication. We show that any

Dynamic Controllability Made Simple.

O(n^{\alpha})