Stefan Schrödl

Inferring Flow of Control in Program Synthesis by Example

We present a supervised, interactive learning technique that infers control structures of computer programs from user-demonstrated traces. A two-stage process is applied: first, a minimal deterministic finite automaton (DFA) M labeled by the instructions of the program is learned from a set of example traces and membership queries to the user. It accepts all prefixes of traces of the target program. The number of queries is bounded by O(k ˙ |M|), with k being the total number of instructions in the initial example traces. In the second step we parse this automaton into a high-level programming language in O(|M|2) steps, replacing jumps by conditional control structures.

Chapter 17 – Vehicle Navigation

Publisher Summary This chapter gives a general introduction to state space search problems in routing applications. Map matching and various speedup techniques are discussed. Navigation is a ubiquitous need to satisfy todays mobility requirements. Current navigation systems assist almost any kind of motion in the physical world including sailing, flying, hiking, driving, and cycling. This success in the mass market has been largely fueled by the advent of the global positioning system (GPS), which provides a fast, accurate, and cost-efficient way to determine ones geographical position anywhere on the Earth. GPS is most useful in combination with a digital map; map matching can provide the user with the information of where he or she is located with regard to it. However, for use in a vehicle, it is not only desirable to know the current position but also to obtain directions of how to get from the current position to a possibly unknown target. To solve this problem, route finding has become a major application area for heuristic search algorithms. This chapter briefly reviews the interplay of search algorithms and other components of navigation systems and discusses particular algorithmic challenges arising in this field.

Dictionary Data Structures

For the enhanced efficiency of A* this chapter discusses different dictionary data structures. Priority queues are provided for integer and total ordered keys. For duplicate elimination, hashing is studied, including provably constant access time. Moreover, maintaining partial states in form of substrings or subsets is considered.

Automatically Created Heuristics

This chapter studies the limits and possibilities of problem abstractions and their relation to heuristic search. As the most important representative of abstraction data structures, it considers pattern databases in a great level of detail.

Automated System Verification

This chapter gives a general introduction to search problems in model checking, Petri nets, and graph transition systems. It also gives a general introduction to automated theorem proving and discusses state space search for proof state–based theorem proving and diagnosis problems.

Linear-Space Search

This chapter first studies breadth-first and single-source shortest paths search on logarithmic space. It then introduces and analyzes different aspects of iterative-deepening A* search. The growth of the search tree is estimated and it is shown that heuristics correspond to a relative decrease of the search depth.

Basic Search Algorithms

This chapter establishes that besides breadth- and depth-first search the (single-source shortest paths) algorithm of Dijkstra is of particular interest, since the heuristic search algorithm A* is a generalization of it. For nonconsistent heuristics already explored nodes are reopened to preserve the optimality of the first solution.

State Space Pruning

Publisher Summary This chapter discusses learning approaches to prune the successor set(s). It studies the exclusion of forbidden states or move sequences and localizing the search using the notion of relevance. The chapter distinguishes between on-the-fly and offline learning. One of the most effective approaches to tackle large problem spaces is to prune (i.e., cutoff branches from) the search tree. There are multiple reasons for pruning. Some branches might not lead to a goal state, others lead to inferior solutions; some result in positions already reached on different paths, and others are redundant; though these might lead to a solution, there are still alternatives that also lead to a solution. All state space pruning techniques reduce the node-branching factor of the search tree such that fewer successor nodes have to be analyzed. Since a smaller part of the state space is generated, pruning saves both search time and space. However, there might be a trade-off between the two. Some techniques require rather complex data structures, such that the maintenance of pruning information may be involved. Static pruning techniques detect pruning knowledge prior to the main search routine. Other pruning rules may not be known to the search algorithm at its start and have to be inferred during the execution of the program. This leads to layered search algorithms. In the top-level search, the search algorithms search for problem solutions, and in frequently invoked lower-level searches, pruning knowledge is refined.

Chapter 8 – External Search

Publisher Summary This chapter studies the integration of disk space into the search, trying to minimize the number of block accesses. It introduces the theory of external memory algorithms and studies disk-based search with the delayed detection of duplicates and its variants. Often search spaces are so large that even in a compressed form they fail to fit into the main memory. During the execution of a search algorithm, only a part of the graph can be processed in the main memory at a time; the remainder is stored on a disk. Most modern operating systems hide secondary memory accesses from the programmer, but offer one consistent address space of virtual memory that can be larger than internal memory. When the program is executed, virtual addresses are translated into physical addresses. Only those portions of the program currently needed for the execution are copied into main memory. Caching and prefetching heuristics have been developed to reduce the number of page faults. By their nature, however, these methods cannot always take full advantage of the locality inherent in algorithms. Algorithms that explicitly manage the memory hierarchy can lead to substantial speedups, since they are more informed to predict and adjust future memory access.

Chapter 7 – Symbolic Search

Publisher Summary This chapter studies symbolic versions for various search algorithms and takes binary decision diagrams to represent and explore sets of states efficiently. Known search refinements are tailored to this setting. The central challenge in scaling-up search is the state/space explosion problem, which denotes that the size of the state space grows exponentially in the number of state variables (problem components). In recent years, symbolic search techniques, originally developed for verification domains, have shown a large impact on improving AI search. The term symbolic search originates in the research area and has been chosen to contrast explicit-state search. The characteristic function of a state set can be much smaller than the number of states it represents. The main advantage of symbolic search is that it operates on the functional representation of both state and actions. This has a dramatic impact on the design of available search algorithms, as known explicit-state algorithms have to be adapted to the exploration of sets of states. Binary decision diagrams (BDDs) are selected as the appropriate data structure for characteristic functions. BDDs are directed, acyclic, and labeled graphs. Roughly speaking, these graphs are restricted deterministic finite automata, accepting the state vectors (encoded in binary) that are contained in the underlying set.