Improvements in finite state machines

Finite State Machine (FSM) based testing methods have a history of over half a century, starting in 1956 with the works on machine identi cation. This was then followed by works checking the conformance of a given implementation to a given speci cation. When it is possible to identify the states of an FSM using an appropriate input sequence, it's been long known that it is possible to generate a Fault Detection Experiment with fault coverage with respect to a certain fault model in polynomial time. In this thesis, we investigate two notions of fault detection sequences; Checking Sequence (CS), Checking Experiment (CE). Since a fault detection sequence (either a CS or a CE) is constructed once but used many times, the importance of having short fault detection sequences is obvious and hence recent works in this eld aim to generate shorter fault detection sequences. In this thesis, we rst investigate a strategy and related problems to reduce the length of a CS. A CS consists several components such as Reset Sequences and State Identi - cation Sequences. All works assume that for a given FSM, a reset sequence and a state identi cation sequence are also given together with the speci cation FSM M. Using the given reset and state identi cation sequences, a CS is formed that gives full fault coverage under certain assumptions. In other words, any faulty implementation N can be identi ed by using this test sequence. In the literature, di erent methods for CS construction take di erent approaches to put these components together, with the aim of coming up with a shorter CS incorporating all of these components. One obvious way of keeping the CS short is to keep components short. As the reset sequence and the state identi cation sequence are the biggest components, having short reset and state identi cation sequences is very important as well. It was shown in 1991 that for a given FSM M, shortest reset sequence cannot be computed in polynomial time if P 6≠NP. Recently it was shown that when the FSM has particular type (\monotonic") of transition structure, constructing one of the shortest reset word is polynomial time solvable. However there has been no work on constructing one of the shortest reset word for a monotonic partially speci ed machines. In this thesis, we showed that this problem is NP-hard. On the other hand, in 1994 it was shown that one can check if M has special type of state identi cation sequence (known as an adaptive distinguishing sequence) in polynomial time. The same work also suggests a polynomial time algorithm to construct a state identi cation sequence when one exists. However, this algorithm generates a state identi cation sequence without any particular emphasis on generating a short one. There has been no work on the generation of state identi cation sequences for complete or partial machines after this work. In this thesis, we showed that construction of short state identi cation sequences is NP-complete and NP-hard to approximate. We propose methods of generating short state identi cation sequences and experimentally validate that such state identi cation sequences can reduce the length of fault detection sequences by 29:2% on the average. Another line of research, in this thesis, devoted for reducing the cost of checking experiments. A checking experiment consist of a set of input sequences each of which aim to test di erent properties of the implementation. As in the case of CSs, a large portion of these input sequences contain state identi cation sequences. There are several kinds of state identi cation sequences that are applicable in CEs. In this work, we propose a new kind of state identi cation sequence and show that construction of such sequences are PSPACE-complete. We propose a heuristic and we perform experiments on benchmark FSMs and experimentally show that the proposed notion of state identi cation sequence can reduce the cost of CEs by 65% in the extreme case. Testing distributed architectures is another interesting eld for FSM based fault detection sequence generation. The additional challenge when such distributed architectures are considered is to generate a fault detection sequence which does not pose controllability or observability problem. Although the existing methods again assume that a state identi cation sequence is given using which a fault detection sequence is constructed, there is no work on how to generate a state identi cation sequence which do not have controllability/observability problem itself. In this thesis we investigate the computational complexities to generate such state identi cation sequences and show that no polynomial time algorithm can construct a state identi cation sequence for a given distributed FSM

Generating minimum height ADSs for partially specified finite state machines

In earlier work, the problem of generating a preset distinguishing sequence from a finite state machine (FSM) was converted into a Boolean formulae to be fed into a SAT solver, with experiments suggesting that such approaches are required as the size of input alphabet grows. In this paper we extend the approach to the minimum height adaptive distinguishing sequence construction problem for partially specified FSMs (PSFMSs), which is known to be an NP- Hard problem. The results of experimentswith randomly generated PSFSMs and case studies from the literature show that SAT solvers can perform better than a previously proposed brute-force algorithm.The Scientific and Technological Research Council of Turkey under the grant reference no B.14.2.TBT.0.06.01-219-115543

Parallel algorithms for generating distinguishing sequences for observable non-deterministic FSMs

A distinguishing sequence (DS) for a finite state machine (FSM) is an input sequence that distinguishes every pair of states of the FSM. There are techniques that generate a test sequence with guaranteed fault detection power and it has been found that shorter test sequence can be produced if DSs are used. Despite these benefits, however, until recently the only published DS generation algorithms have been for deterministic FSMs. This paper develops a massively parallel algorithm, which can be used in GPU Computing, to generate DSs from partial observable non-deterministic FSMs. We also present the results of experiments using randomly generated FSMs and some benchmark FSMs. The results are promising and indicate that the proposed algorithm can derive DSs from partial observable non-deterministic FSMs with 32,000 states in an acceptable amount of time.This work is supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under Grant #1059B191400424 and by the NVIDIA corporation

ON EXPRESSIVENESS, INFERENCE, AND PARAMETER ESTIMATION OF DISCRETE SEQUENCE MODELS

Huge neural autoregressive sequence models have achieved impressive performance across different applications, such as NLP, reinforcement learning, and bioinformatics. However, some lingering problems (e.g., consistency and coherency of generated texts) continue to exist, regardless of the parameter count. In the first part of this thesis, we chart a taxonomy of the expressiveness of various sequence model families (Ch 3). In particular, we put forth complexity-theoretic proofs that string latent-variable sequence models are strictly more expressive than energy-based sequence models, which in turn are more expressive than autoregressive sequence models. Based on these findings, we introduce residual energy-based sequence models, a family of energy-based sequence models (Ch 4) whose sequence weights can be evaluated efficiently, and also perform competitively against autoregressive models. However, we show how unrestricted energy-based sequence models can suffer from uncomputability; and how such a problem is generally unfixable without knowledge of the true sequence distribution (Ch 5). In the second part of the thesis, we study practical sequence model families and algorithms based on theoretical findings in the first part of the thesis. We introduce neural particle smoothing (Ch 6), a family of approximate sampling methods that work with conditional latent variable models. We also introduce neural finite-state transducers (Ch 7), which extend weighted finite state transducers with the introduction of mark strings, allowing scoring transduction paths in a finite state transducer with a neural network. Finally, we propose neural regular expressions (Ch 8), a family of neural sequence models that are easy to engineer, allowing a user to design flexible weighted relations using Marked FSTs, and combine these weighted relations together with various operations

Combinatorial Problems in Online Advertising

Electronic commerce or eCommerce refers to the process of buying and selling of goods and services over the Internet. In fact, the Internet has completely transformed traditional media based advertising so much so that billions of dollars of advertising revenue is now flowing to search companies such as Microsoft, Yahoo! and Google. In addition, the new advertising landscape has opened up the advertising industry to all players, big and small. However, this transformation has led to a host of new problems faced by the search companies as they make decisions about how much to charge for advertisements, whose ads to display to users, and how to maximize their revenue. In this thesis we focus on an entire suite of problems motivated by the central question of "Which advertisement to display to which user?". Targeted advertisement happens when a user enters a relevant search query. The ads are usually displayed on the sides of the search result page. Internet advertising also takes place by displaying ads on the side of webpages with relevant content. While large advertisers (e.g. Coca Cola) pursue brand recognition by advertisement, small advertisers are happy with instant revenue as a result of a user following their ad and performing a desired action (e.g. making a purchase). Therefore, small advertisers are often happy to get any ad slot related to their ad while large advertisers prefer contracts that will guarantee that their ads will be delivered to enough number of desired users. We first focus on two problems that come up in the context of small advertisers. The first problem we consider deals with the allocation of ads to slots considering the fact that users enter search queries over a period of time, and as a result the slots become available gradually. We use a greedy method for allocation and show that the online ad allocation problem with a fixed distribution of queries over time can be modeled as maximizing a continuous non-decreasing submodular sequence function for which we can guarantee a solution with a factor of at least (1- 1/e) of the optimal. The second problem we consider is query rewriting problem in the context of keyword advertisement. This problem can be posed as a family of graph covering problems to maximize profit. We obtain constant-factor approximation algorithms for these covering problems under two sets of constraints and a realistic notion of ad benefit. We perform experiments on real data and show that our algorithms are capable of outperforming a competitive baseline algorithm in terms of the benefit due to rewrites. We next consider two problems related to premium customers, who need guaranteed delivery of a large number of ads for the purpose of brand recognition and would require signing a contract. In this context, we consider the allocation problem with the objective of maximizing either revenue or fairness. The problems considered in this thesis address just a few of the current challenges in e-Commerce and Internet Advertising. There are many interesting new problems arising in this field as the technology evolves and online-connectivity through interactive media and the internet become ubiquitous. We believe that this is one of the areas that will continue to receive greater attention by researchers in the near future

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Cryptography based on the Hardness of Decoding

This thesis provides progress in the fields of for lattice and coding based cryptography. The first contribution consists of constructions of IND-CCA2 secure public key cryptosystems from both the McEliece and the low noise learning parity with noise assumption. The second contribution is a novel instantiation of the lattice-based learning with errors problem which uses uniform errors

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Checking sequence construction using multiple adaptive distinguishing sequences

A new method for constructing a checking sequence for finite state machine (FSM) based testing is introduced. Unlike its predecessors, which are based on state recognition using a single state identification sequence, our approach makes use of multiple state identification sequences. Using multiple state identification sequences provides an opportunity to construct shorter checking sequences, based on a greedy approach of choosing a state identification sequence that best suits our goal at different points during the construction of the checking sequence. Our approach has two phases. In the first phase, a test sequence [symbol]is constructed using multiple state identification sequences. The sequence [symbol] is not guaranteed to be a checking sequence, however it is further extended to a checking a sequence by the second phase of our method. We present the results of an experimental study showing that our two phase approach produces shorter checking sequences than the previously published methods